Publications

1. Memoir: Cardona, D., Ruzhansky, M. Subelliptic pseudo-differential operators and Fourier integral operators on compact Lie groups.
   Project Euclid Link | Math. Soc. Japan link |
   MSJ Memoirs, Math. Soc. Japan, 44: 175pp. (2025). arXiv:2008.09651.
   Link 

2. Book: Cardona, D., Kähler, U. (Editors). Analysis and PDE in Developing Countries, Proceedings of the ISAAC-ICMAM Conference 2024. Research Perspectives: Ghent Analysis and PDE Center,
   Trends in Mathematics, Birkhäuser 2026, to appear.
   Link

3. 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.
   Link

4. Cardona, D. L2-Maximal functions on graded Lie groups,
   IMRN (Int. Math. Res. Not.), Vol. 2024 (14), 10776-10789, (2024). arXiv:2401.10830.
   Link

5. 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.
   Link

6. 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.
   Link 

7. 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.
   Link

8. 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.
   Link

9. Cardona, D., Ruzhansky, M. Oscillating singular integral operators on graded Lie groups revisited, to appear in
   J. Lie Theory, arXiv:2201.12881.
   Link

10. 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.
    Link

11. 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.
    Link

12. Cardona, D., Ruzhansky, M. Oscillating singular integral operators on compact Lie groups revisited,
    Math. Z., Vol. 303, 26 (2023). arXiv:2202.10531.
    Link

13. Cardona, D., Chatzakou, M., Delgado, J., Ruzhansky, M. Degenerate Schrödinger equations with irregular potentials, to appear in:
    Anal. Appl., arXiv:2302.02413.
    Link

14. 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.
    Link

15. 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.
    Link

16. 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.
    Link

17. 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.
    Link

18. Cardona, D., Ruzhansky, M. Fourier multipliers for Triebel-Lizorkin spaces on compact Lie groups,
    Collect. Math., Vol. 73, 477–504, (2022). arXiv:2101.12314.
    Link

19. 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.
    Link

20. 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.
    Link

21. 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.
    Link

22. 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.
    Link

23. 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.
    Link

24. 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.
    Link

25. 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.
    Link

26. 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.
    Link

27. Cardona, D. Weighted boundedness for a class of local lacunary maximal operators,
    J. Math. Sci. 289, 926–943 (2025).
    Link

28. 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.
    Link

29. 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.
    Link

30. 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.
    Link

31. 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.
    Link

32. Cardona, D., Esquivel, L. On the Benjamin Ono equation in the half line,
    Nonlinear Analysis, Vol. 212, (2021), Art. 112427. arXiv:2101.06992.
    Link

33. 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.
    Link

34. 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.
    Link

35. Cardona, D., Delgado, J., Ruzhansky, M. Determinants and Plemelj-Smithies formulas,
    Monatsh. Math., Vol. 199, 459–482, (2022). arXiv:2012.13216.
    Link

36. 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.
    Link

37. 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.
    Link

38. 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.
    Link

39. 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.
    Link

40. 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.
    Link

41. 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.
    Link

42. Cardona, D. On the multiplier problem for the ball on graded Lie groups, submitted. arXiv:2012.11057.
    Link

43. Cardona, D., Delgado, J., Muñoz Tello, A. Gateaux differentiability of the Sobolev norm W(k,1)(M) on compact Riemannian manifolds,
    J. Anal.  to appear.
    Link

44. 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.
    Link

45. 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.
    Link
    
    

46. 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.
    Link

47. 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.
    Link

48. 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.
    Link

49. 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.
    Link

50. 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.
    Link

51. Cardona, D. The weak type (1,p) for convolution operators on locally compact groups, arXiv:1803.02413.
    Link

52. 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).
    Link

53. 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.
    Link

54. 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.
    Link

55. 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.
    Link

56. Cardona, D. On the boundedness of periodic pseudo-differential operators,
    Monatsh. Math., Vol. 185(2), 189-206, (2018). arXiv:1701.08184.
    Link

57. 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).
    Link

58. Cardona, D., Ruzhansky, M. Multipliers for Besov spaces on graded Lie groups,
    C. R. Math. Acad. Sci. Paris, Vol. 355, (4), 400-405, (2017).
    Link

59. 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.
    Link

60. Cardona, D. Hölder-Besov boundedness for periodic pseudo-differential operators,
    J. Pseudo-Differ. Oper. Appl., Vol. 8, (1), 13–34, (2016). arXiv:1609.03514.
    Link

61. Cardona, D. Besov continuity for Multipliers defined on compact Lie groups,
    Palest. J. Math., Vol. 5, (2), 35-44, (2016).
    Link

62. Cardona, D. On the singular values of the Fox-Li operator,
    J. Pseudo-Differ. Oper. Appl., Vol. 6, (4), 427-438, (2015).
    Link

63. Cardona, D. Invertibility for a class of Fourier multipliers,
    J. Pseudo-Differ. Oper. Appl., Vol. 6, (2), 215-225, (2015).
    Link

64. 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).
    Link

65. Cardona, D. Hölder estimates for pseudo-differential operators on T1,
    J. Pseudo-Differ. Oper. Appl., Vol. 5 (4), 517-525, (2014).
    Link

66. Cardona, D. L∞-BMO bounds for pseudo-multipliers associated with the harmonic oscillator,
    Rev. Colombiana Mat., Vol. 54(2), 93-108, (2020).
    Link

67. 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).
    Link

68. 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).
    Link

69. 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).
    Link

70. Cardona, D. On the nuclear trace of Fourier Integral Operators,
    Rev. Integr. temas Mat., Vol. 37(2), 219-249, (2019). arXiv:1807.08389.
    Link

71. 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.
    Link

72. 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).
    Link

73. 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).
    Link

74. Cardona, D. A note on the Fourier transform in Hölder spaces,
    Rev. Elementos, Vol. 6(6), 61-66, (2016).
    Link

75. Cardona, D. Una nota sobre la transformada de Fourier en espacios de Hölder,
    Miscelánea Mat., No. 61, 11–20, (2015/16).
    Link

76. Cardona, D. Estimativos L2 para una clase de operadores pseudodiferenciales definidos en el toro,
    Rev. Integr. Temas Mat., Vol. 31, (2), 142-157, (2013).
    Link

77. Cardona, D. Invertibilidad de operadores pseudo-diferenciales definidos en Zn,
    Lect. Mat., Vol. 34 (2), 179-186, (2013).
    Link

78. Cardona, D. Operadores pseudodiferenciales definidos en medidas de Borel,
    Rev. Integr. Temas Mat., Vol. 31 (1), 25-42, (2013).
    Link
    
    Chapters in Books
    
    

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

80. 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.
    Link

81. Cardona, D., Mapping properties of weighted Maximal Functions, to appear in:
    Trends in Mathematics.
    Link

82. Cardona, D., Boundedness of Fourier integral operators revisited, to appear in Trends in Mathematics.
    Link

83. Cardona, D., Martínez, M.A. (2026). Boundedness of Pseudo-Differential Operators on the Torus via Kernel Estimates. In: Cardona Sanchez, D., Grajales, B. (eds).
    Analysis and PDE in Latin America. ICMAM 2024.  Trends in Mathematics. vol 15. Birkhäuser, Cham.
    Link

84. Cardona, D., Castro, T., Correa, S., De la Cruz, R. (2026). Mathematics and Memory: A Seminar of Analysis and Differential Equations for Latin America.
    Analysis and PDE in Latin America. ICMAM 2024.  Trends in Mathematics. vol 15. Birkhäuser, Cham.
    Link

85. 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.
    Link

86. 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.
    Link

87. 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.
    Link

88. 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.
    Link

89. 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.
    Link

90. 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.
    Link

91. 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.
    Link

92. 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.
    Link
    
    Preprints
    
    

93. Cardona, D., Obeng-Denteh, W., Opoku, F. Hyperbolic partial differential equations with complex characteristics on Fourier Lebesgue spaces, submitted. 

94. Cardona, D., Local smoothing estimates for bilinear Fourier integral operators, submitted.  arXiv:2601.15667.
    Link 

95. Cardona, D., Obeng-Denteh, W., Opoku, F. Boundedness of Fourier integral operators with complex phases on Fourier Lebesgue spaces, submitted. arXiv:2512.24854.
    Link 

96. Cardona, D., Martinez, M. A. Boundedness of pseudo-differential operators on the torus revisited, III. submitted. arXiv:2508.13338
    Link

97. Cardona, D. Riesz-Means Bounds for Functional-Difference operators on mirror curves, submitted. arXiv:2508.07433.
    Link

98. Cardona, D., Martinez, M. A. Boundedness of pseudo-differential operators on the torus revisited, II. submitted. arXiv:2505.01573
    Link

99. 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.
    Link

100. Cardona, D., Kumar, V., Ruzhansky, M. Pseudo-differential operators on homogeneous vector-bundles over compact homogeneous manifolds, submitted. arXiv:2403.08990.
     Link

101. Cardona, D., Ruzhansky, M. The weak (1,1) boundedness of Fourier integral operators with complex phases, submitted. arXiv:2402.09054.
     Link

102. Cardona, D. Estimates for the full maximal function on graded Lie groups, submitted. arXiv:2401.07086.
     Link

103. Cardona, D. Characterisation of certain Schatten-von Neumann classes on the torus, submitted.
     Link

104. Cardona, D., Grajales, B., Ruzhansky, M. On the sharpness of Strichartz estimates and spectrum of compact Lie groups, submitted. arXiv:2302.04139.
     Link

105. Cardona, D. Spectral inequalities for elliptic pseudo-differential operators on closed manifolds, submitted. arXiv:2209.10690.
     Link

106. Cardona, D., Duduchava, R., Hendricks, A., Ruzhansky, M. Global pseudo-differential operators on the Lie group G=(−1,1)n, submitted. arXiv:2209.09751.
     Link

107. Cardona, D., Ruzhansky, M. Boundedness of oscillating singular integrals on Lie groups of polynomial growth, submitted. arXiv:2201.12883.
     Link

108. 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.
     Link

109. 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.
     Link

110. Cardona, D., Ruzhansky, M. Fourier multipliers for Triebel-Lizorkin spaces on graded Lie groups, submitted. arXiv:2101.05856.
     Link