Duván Cardona - Publications

Short description: I have published my mathematical research in several international journals, including: IMRN (International Mathematics Research Notices), The Journal of Geometric Analysis, Quarterly Journal of Mathematics, Mathematische Zeitschrift, New York Journal of Mathematics, Pure and Applied Analysis, Forum Mathematicum (FORUM), Journal of Lie Theory, Potential Analysis, J. Fourier Analysis and Appl., Mathematische Nachrichten, Journal of Evolution Equations, Nonlinear Analysis, C. R. Math. Acad. Sci. Paris., etc. You can have a look to my books here!

Below you will find a complete list of my publications:

Publications

Cardona, D., Martinez, M. A. Boundedness of pseudo-differential operators on the torus revisited, I.,
J. Math. Anal. Appl., 554, Vol. 2, No. 129959, 2025. arXiv:2502.20575.
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Hurtado Quiceno, Andrea, V., Cardona, D. The constant in the Sobolev inequality and the boundedness of subelliptic operators on compact Lie groups,
Commun. Anal. Mech. 17(4): 878–897, 2025.
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Cardona, D., Chatzakou, M., Delgado, J., Kumar, V., Ruzhansky, M. Anharmonic semigroups and applications to global well-posedness of nonlinear heat equations, to appear in:
J. Math. Phys., Vol. 66 (2025), paper no. 081509. arXiv:2401.13750.
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Cardona, D., Ruzhansky, M. Oscillating singular integral operators on graded Lie groups revisited, to appear in
J. Lie Theory, arXiv:2201.12881.
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Cardona, D., Chatzakou, M., Delgado, J., Ruzhansky, M. Degenerate Schrödinger equations with irregular potentials, to appear in:
Anal. Appl., arXiv:2302.02413.
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Cardona, D., Kirilov, A., de Moraes, W. A., Pedroso, Kowacz, A. On the Sobolev boundedness of vector fields on compact Riemannian manifolds,
J. Pseudo-Differ. Oper. Appl. 16, 52 (2025). arXiv:2404.00182.
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Cardona, D., Kumar, V., Ruzhansky, M., Tokmagambetov, N. Lp-Lq boundedness of pseudo-differential operators on smooth manifolds and its applications to nonlinear equations,
Ann. Funct. Anal., 6 (2025), no. 3, 50. arXiv:2005.04936.
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Book: Cardona, D., Grajales, B. (Editors). Analysis and PDE in Latin America, ICMAM 2023-2024, Research Perspectives: Ghent Analysis and PDE Center,
Trends in Mathematics, Birkhäuser, to appear.
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Cardona, D., Kumar, V., Ruzhansky, M. Lp-Lq-Boundedness of pseudo-differential operators on graded Lie groups,
New York J. Math. 31 (2025), 722-748. arXiv:2307.16094.
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Cardona, D., Kumar, V., Ruzhansky, M., Tokmagambetov, N. Expansion of traces and Dixmier traceability for global pseudo-differential operators on manifolds with boundary,
Adv. Oper. Theory. 10 (2025), 10(53). arXiv:2101.05883.
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Cardona, D. L2-Maximal functions on graded Lie groups,
IMRN (Int. Math. Res. Not.), Vol. 2024 (14), 10776-10789, (2024). arXiv:2401.10830.
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Cardona, D. Weighted boundedness for a class of local lacunary maximal operators,
J. Math. Sci. 289, 926–943 (2025).
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Cardona, D., Delgado, J., Ruzhansky, M. Estimates for sums of eigenfunctions of elliptic pseudo-differential operators on compact Lie groups,
J. Geom. Anal., Vol. 34, 374 (2024). arXiv:2209.12092.
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Cardona, D., Delgado, J., Ruzhansky, M. Boundedness of the dyadic maximal function on graded Lie groups,
Quart. J. Math., Vol. 75(3), 809-834, (2024). arXiv:2301.08964.
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Cardona, D., Federico, S., Ruzhansky, M. Subelliptic sharp Gårding inequality on compact Lie groups,
Pure Appl. Anal., Vol. 6, No. 2, 455–485, (2024). arXiv:2110.00838.
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Cardona, D., Chatzakou, M., Ruzhansky, M., Toft, J. Schatten-von Neumann properties for Hörmander classes on compact Lie groups, to appear in:
Forum Math., arXiv:2301.04044.
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PhD Thesis: Cardona Sanchez, D. “Contributions to the theory of pseudo-differential operators: from compact to graded Lie groups,” Ghent University. Faculty of Sciences, Ghent, Belgium, 2023.
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Cardona, D., Delgado, J., Grajales, B., Ruzhansky, M. Control of the Cauchy problem on Hilbert spaces: a global approach via symbol criteria,
Commun. Pure Appl. Anal., Vol. 22(11), 3295-3329, (2023). arXiv:2301.08999.
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Cardona, D., Delgado, J., Ruzhansky, M. A note on the local Weyl formula on compact Lie groups,
J. Lie Theory, 34(1), 237–248, (2024). arXiv:2210.00311.
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Cardona, D., Ruzhansky, M. Björk-Sjölin condition for strongly singular convolution operators on graded Lie groups,
Math. Z., 302, 1957–1981, (2022). arXiv:2205.03456.
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Cardona, D., Delgado, J., Ruzhansky, M. Drift diffusion equations with fractional diffusion on compact Lie groups,
J. Evol. Equ., No. 22, Vol. 84, (2022). arXiv:2205.02320.
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Cardona, D., Ruzhansky, M. Oscillating singular integral operators on compact Lie groups revisited,
Math. Z., Vol. 303, 26 (2023). arXiv:2202.10531.
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Cardona, D., Ruzhansky, M. Sharpness of Seeger-Sogge-Stein orders for the weak (1,1) boundedness of Fourier integral operators,
Arch. Math., Vol. 119, 189–198 (2022). arXiv:2104.09695.
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Book: Cardona, D., Grajales, B. (Editors). Analysis and PDE in Latin America, ICMAM 2022 Latin America, Research Perspectives: Ghent Analysis and PDE Center,
Trends in Mathematics, Birkhäuser, 2024.
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Cardona, D., Delgado, J., Kumar, V., Ruzhansky, M. Lp-Lq-Boundedness of pseudo-differential operators on compact Lie groups,
Osaka J. Math., 62(4), 587-608, (2025). arXiv:2310.16247.
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Cardona, D., Ruzhansky, M. Fourier multipliers for Triebel-Lizorkin spaces on compact Lie groups,
Collect. Math., Vol. 73, 477–504, (2022). arXiv:2101.12314.
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Cardona, D., Esquivel, L. On the Benjamin Ono equation in the half line,
Nonlinear Analysis, Vol. 212, (2021), Art. 112427. arXiv:2101.06992.
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Cardona, D., Kumar, V., Ruzhansky, M., Tokmagambetov, N. Global Functional calculus, lower/upper bounds and evolution equations on manifolds with boundary,
Adv. Oper. Theory, 8, 50 (2023). arXiv:2101.02519.
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Cardona, D., Kowacs, A. Global hypoellipticity of G-invariant operators on homogeneous vector-bundles,
J. Pseudo-Differ. Oper. Appl., Vol. 16, 23 (2025). arXiv:2310.17288.
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Cardona, D., Delgado, J., Ruzhansky, M. Determinants and Plemelj-Smithies formulas,
Monatsh. Math., Vol. 199, 459–482, (2022). arXiv:2012.13216.
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Book: Cardona, D., Restrepo, J., Ruzhansky, M. (Editors). Extended Abstracts 2021/2022, Methusalem Lectures, Research Perspectives: Ghent Analysis and PDE Center,
Trends in Mathematics,. Birkhäuser, 2023.
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Memoir: Cardona, D., Ruzhansky, M. Subelliptic pseudo-differential operators and Fourier integral operators on compact Lie groups, to appear in:
MSJ Memoirs, Math. Soc. Japan, arXiv:2008.09651.
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Cardona, D., Delgado, J., Ruzhansky, M. Lp-bounds for pseudo-differential operators on graded Lie groups,
J. Geom. Anal., Vol. 31, 11603-11647, (2021). arXiv:1911.03397.
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Cardona, D., Ruzhansky, M. Littlewood-Paley theorem, Nikolskii inequality, Besov spaces, Fourier and spectral multipliers on graded Lie groups,
Potential Analysis, Vol. 60, 965-1005, (2024). arXiv:1610.04701.
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Cardona, D., Messiouene, R., Senoussaoui, A. Periodic Fourier integral operators in Lp spaces,
C. R. Math. Acad. Sci. Paris, Vol. 359 (5), (2021), 547-553.
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Cardona, D., Esquivel, L. Sharp Strichartz estimates for the Schrödinger equation on the sphere,
J. Pseudo-Differ. Oper. Appl., Vol. 12, 23 (2021). arXiv:2006.08165.
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Cardona, D., Kumar, V. The nuclear trace of vector-valued pseudo-differential operators with applications to Index theory,
Math. Nachr., Vol. 294(9), 1657-1683, (2021). arXiv:1901.10010.
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Cardona, D., Ruzhansky, M. Boundedness of pseudo-differential operators in subelliptic Sobolev and Besov spaces on compact Lie groups,
Complex Var. Elliptic Equ., Vol. 69(7), 1049–1082, (2023). arXiv:1901.06825.
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Cardona, D., Ruzhansky, M. Hörmander condition for pseudo-multipliers associated to the harmonic oscillator,
Hokkaido Math. J. Vol. 54, No. 1, (2025). arXiv:1810.01260.
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Cardona, D. Sharp estimates for the Schrödinger equation associated to the twisted Laplacian,
Rep. Math. Phys., Vol. 85(1), 29-39, (2020). arXiv:1810.02940.
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Cardona, D. On the multiplier problem for the ball on graded Lie groups, submitted. arXiv:2012.11057.
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Cardona, D. Lp-estimates for a Schrödinger equation associated with the harmonic oscillator,
Electron. J. Differential Equations, Vol. (2019), No. 20, pp. 1-10. arXiv:1808.02906.
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Cardona, D., Kumar, V. Lp-boundedness and Lp-nuclearity of multilinear pseudo-differential operators on Zn and the torus Tn,
J. Fourier Anal. Appl., Vol. 25 (6), 2973-3017, (2019). arXiv:1809.08380.
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Cardona, D., Messiouene, R., Senoussaoui, A. Lp-bounds for Fourier integral operators on the torus,
Complex Var. Elliptic Equ., 69(2), 252-269, (2022). arXiv:1807.09892.
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Cardona, D. Pseudo-differential operators in Hölder spaces revisited. Weyl-Hörmander calculus and Ruzhansky-Turunen classes,
Mediterr. J. Math., 16, no. 6. Art. 148, 17 pp. (2019). arXiv:1806.09245.
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Cardona, D., Kumar, V., Del Corral, C. Dixmier traces for discrete pseudo-differential operators,
J. Pseudo-Differ. Oper. Appl., Vol. 11, 647-656, (2020). arXiv:1911.03924.
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Cardona, D. Besov continuity for global operators on compact Lie groups: the critical case p=q=∞,
Trans. A. Razmadze Math. Inst, Vol. 172 (3), 354-360, (2018). arXiv:1807.00952.
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Cardona, D. On the index of pseudo-differential operators on compact Lie groups,
J. Pseudo-Differ. Oper. Appl., Vol. 10 (2), 285-305 (2019). arXiv:1805.10404.
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Cardona, D. The weak type (1,p) for convolution operators on locally compact groups, arXiv:1803.02413.
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Cardona, D., Delgado, J., Ruzhansky, M. Well-posedness for a class of pseudo-differential hyperbolic equations on the torus,
Aequat. Math., Vol. 98, 1019–1038 (2024).
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Cardona, D. Pseudo-differential operators on Zn with applications to discrete fractional integral operators,
Bull. Iran. Math. Soc., 45 (4), 1227–1241, (2019). arXiv:1803.00231.
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Cardona, D., E. Samuel Barraza. Characterization of nuclear pseudo-multipliers associated to the harmonic oscillator,
UPB Sci. Bull. A: Appl. Math. Phys., Vol. 80 (4), 163-172, (2018). arXiv:1803.00903.
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Cardona, D. Nuclear pseudo-differential operators in Besov spaces on compact Lie groups,
J. Fourier Anal. Appl., Vol. 23, (5), 1238-1262, (2017). arXiv:1610.09042.
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Cardona, D. On the boundedness of periodic pseudo-differential operators,
Monatsh. Math., Vol. 185(2), 189-206, (2018). arXiv:1701.08184.
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Cardona, D. Besov continuity of pseudo-differential operators on compact Lie groups revisited,
C. R. Math. Acad. Sci. Paris, Vol. 355, (5), 533–537, (2017).
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Cardona, D., Ruzhansky, M. Multipliers for Besov spaces on graded Lie groups,
C. R. Math. Acad. Sci. Paris, Vol. 355, (4), 400-405, (2017).
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Cardona, D. Besov continuity for pseudo-differential operators on compact homogeneous manifolds,
J. Pseudo-Differ. Oper. Appl., Vol. 9, (4), 861-880, (2018). arXiv:1607.00689.
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Cardona, D. Hölder-Besov boundedness for periodic pseudo-differential operators,
J. Pseudo-Differ. Oper. Appl., Vol. 8, (1), 13–34, (2016). arXiv:1609.03514.
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Cardona, D. Besov continuity for Multipliers defined on compact Lie groups,
Palest. J. Math., Vol. 5, (2), 35-44, (2016).
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Cardona, D. On the singular values of the Fox-Li operator,
J. Pseudo-Differ. Oper. Appl., Vol. 6, (4), 427-438, (2015).
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Cardona, D. Invertibility for a class of Fourier multipliers,
J. Pseudo-Differ. Oper. Appl., Vol. 6, (2), 215-225, (2015).
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Cardona, D. Weak type (1,1) bounds for a class of periodic pseudo-differential operators,
J. Pseudo-Differ. Oper. Appl., Vol. 5(4), 507-515, (2014).
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Cardona, D. Hölder estimates for pseudo-differential operators on T1,
J. Pseudo-Differ. Oper. Appl., Vol. 5 (4), 517-525, (2014).
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Cardona, D. L∞-BMO bounds for pseudo-multipliers associated with the harmonic oscillator,
Rev. Colombiana Mat., Vol. 54(2), 93-108, (2020).
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Barraza, E. Samuel., Rivas, E., Cardona, D. A data structure to represent data sets with more than one order relation like polygons,
Contemporary Engineering Sciences, Vol. 10, (15), 739-750, (2017).
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Cardona, D. A note on the Stein restriction conjecture and the restriction problem on the torus, E. J. Math. Anal. Appl., Vol. 8(2), 165-171, (2020).
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Cardona, D., Kumar, V. Multilinear analysis for discrete and periodic pseudo-differential operators in Lp spaces,
Rev. Integr. temas Mat., Vol. 36(2), 151-164, (2018).
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Cardona, D. On the nuclear trace of Fourier Integral Operators,
Rev. Integr. temas Mat., Vol. 37(2), 219-249, (2019). arXiv:1807.08389.
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Cardona, D. A brief description of operators associated to the quantum harmonic oscillator on Schatten-von Neumann classes,
Rev. Integr. Temas Mat., Vol. 36(1), 49-57, (2018). arXiv:1803.07924.
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Cardona, D. Weak type (1,1) bounds for a class of operators with discrete kernel,
Rev. Integr. Temas. Mat., Vol. 33 (1), 51-62, (2015).
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Cardona, D., Del Corral, C. The Dixmier trace and the Wodzicki residue for pseudo-differential operators on compact manifolds,
Rev. Integr. Temas. Mat., Vol. 38 (1), 67-79, (2020).
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Cardona, D. A note on the Fourier transform in Hölder spaces,
Rev. Elementos, Vol. 6(6), 61-66, (2016).
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Cardona, D. Una nota sobre la transformada de Fourier en espacios de Hölder,
Miscelánea Mat., No. 61, 11–20, (2015/16).
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Cardona, D. Estimativos L2 para una clase de operadores pseudodiferenciales definidos en el toro,
Rev. Integr. Temas Mat., Vol. 31, (2), 142-157, (2013).
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Cardona, D. Invertibilidad de operadores pseudo-diferenciales definidos en Zn,
Lect. Mat., Vol. 34 (2), 179-186, (2013).
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Cardona, D. Operadores pseudodiferenciales definidos en medidas de Borel,
Rev. Integr. Temas Mat., Vol. 31 (1), 25-42, (2013).
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Chapters in Books

Cardona, D., Martinez, M. A. Boundedness of pseudo-differential operators on the torus via kernel estimates, to appear in Trends in Mathematics.

Cardona, D., Martinez, M. A. Boundedness of toroidal pseudo-differential operators on Hardy spaces, to appear in Trends in Mathematics.

Cardona, D., Castro, T., Correa, S., De la Cruz, R., Mathematics and Memory: A Seminar of Analysis and Differential Equations for Latin America, to appear in: Trends in Mathematics.
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Cardona, D., Hurtado Quiceno, Andrea, V. Sobolev inequality and mapping properties of pseudo-differential operators on compact Lie groups, to appear in Trends in Mathematics.
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Cardona, D., Mapping properties of weighted Maximal Functions, to appear in Trends in Mathematics.
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Cardona, D., Boundedness of Fourier integral operators revisited, to appear in Trends in Mathematics.
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Cardona, D., Mapping Properties of Maximal Functions on Graded Lie Groups. In: Avetisyan, Z., Ruzhansky, M., Vagharshakyan, A. (eds)
Analysis, PDEs, and Applications. GMG 2024. Trends in Mathematics., vol 13. Birkhäuser, Cham.
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Cardona, D., Duduchava, R., Hendrickx, A., Ruzhansky, M. Generic Bessel Potential Spaces on Lie Groups,
Tbilisi Analysis and PDE Seminar. TAPDES 2023. Trends in Mathematics, Vol 7. Birkhäuser, Cham.
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Cardona, D., Kowacs, A. Global hypoellipticity on homogeneous vector bundles: necessary and sufficient conditions,
Modern Problems in PDEs and Applications. MWCAPDE 2023. Trends in Mathematics, Vol 4. Birkhäuser, Cham.
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Cardona, D. Schatten-von Neumann classes Sp on the torus for 0 < p ≤ 2. In: Ruzhansky, M., Van Bockstal, K. (eds).
Extended Abstracts 2021/2022. APDEGS 2021. Trends in Mathematics, vol 2. Birkhäuser, Cham.
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Cardona, D. The Wodzicki residue for pseudo-differential operators on compact Lie groups, In: Ruzhansky, M., Wirth, J. (eds).
Harmonic Analysis and Partial Differential Equations. 2022. Trends in Mathematics, Birkhäuser, Cham.. arXiv:2201.12336.
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Cardona, D. The Index of Toeplitz Operators on Compact Lie Groups and on Simply Connected Closed 3-Manifolds. In: Kähler, U., Reissig, M., Sabadini, I., Vindas, J. (eds)
Analysis, Applications, and Computations. ISAAC 2021. Trends in Mathematics. Birkhäuser, Cham.
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Barraza, E. Samuel., Cardona, D. On nuclear Lp multipliers associated to the harmonic oscillator, in:
Analysis in Developing Countries, Springer Proceedings in Mathematics & Statistics, Springer, Imperial College London, UK, 2016. , M. Ruzhansky and J. Delgado (Eds), (2019). arXiv:1703.07453.
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Cardona, D., Del Corral, C. The Dixmier trace and the non-commutative residue for multipliers on compact manifolds. In: Georgiev V., Ozawa T., Ruzhansky M., Wirth J. (eds)
Advances in Harmonic Analysis and Partial Differential Equations. Trends in Mathematics. Birkhäuser, Cham. arXiv:1703.07453.
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Preprints

Cardona, D., Martinez, M. A. Boundedness of pseudo-differential operators on the torus revisited, III. submitted. arXiv:2508.13338
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Cardona, D. Riesz-Means Bounds for Functional-Difference operators on mirror curves, submitted. arXiv:2508.07433.
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Cardona, D., Martinez, M. A. Boundedness of pseudo-differential operators on the torus revisited, II. submitted. arXiv:2505.01573
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Cardona, D., Delgado, J., Ruzhansky, M. Nuclearity, Schatten-von Neumann classes, distribution of eigenvalues and Lp-Lq-boundedness of Fourier integral operators on compact manifolds, submitted. arXiv:2408.06833.
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Cardona, D., Kumar, V., Ruzhansky, M. Pseudo-differential operators on homogeneous vector-bundles over compact homogeneous manifolds, submitted. arXiv:2403.08990.
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Cardona, D., Ruzhansky, M. The weak (1,1) boundedness of Fourier integral operators with complex phases, submitted. arXiv:2402.09054.
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Cardona, D. Estimates for the full maximal function on graded Lie groups, submitted. arXiv:2401.07086.
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Cardona, D. Characterisation of certain Schatten-von Neumann classes on the torus, submitted.
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Cardona, D., Delgado, J., Muñoz Tello, A. Gateaux differentiability of the Sobolev norm W(k,1)(M) on compact Riemannian manifolds, submitted.
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Cardona, D., Grajales, B., Ruzhansky, M. On the sharpness of Strichartz estimates and spectrum of compact Lie groups, submitted. arXiv:2302.04139.
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Cardona, D. Spectral inequalities for elliptic pseudo-differential operators on closed manifolds, submitted. arXiv:2209.10690.
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Cardona, D., Duduchava, R., Hendricks, A., Ruzhansky, M. Global pseudo-differential operators on the Lie group G=(−1,1)n, submitted. arXiv:2209.09751.
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Cardona, D., Ruzhansky, M. Boundedness of oscillating singular integrals on Lie groups of polynomial growth, submitted. arXiv:2201.12883.
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Cardona, D., Delgado, J., Ruzhansky, M. Analytic functional calculus and Gårding inequality on graded Lie groups with applications to diffusion equations, submitted. arXiv:2111.07469.
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Cardona, D., Delgado, J., Ruzhansky, M. Dixmier traces, Wodzicki residues, and determinants on compact Lie groups: the paradigm of the global quantisation, submitted. arXiv:2105.14949.
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Cardona, D., Ruzhansky, M. Fourier multipliers for Triebel-Lizorkin spaces on graded Lie groups, submitted. arXiv:2101.05856.
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