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, to appear in:
Commun. Anal. Mech.
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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, to appear in
Osaka J. Math., 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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