My research concerns problems from Harmonic Analysis and Partial Differential Equations.

Publications 

• Preprints

  1. J. Lee, S. Lee, L. Roncal, Strichartz and local smoothing estimates for the fractional Schrödinger equations over fractal time, arXiv:2508.16102

  2. S. Lee, L. Roncal, F. Zhang, S. Zhao, Endpoint estimates for the fractal circular maximal function and related local smoothing, arXiv:2506.20390

  3. D. Mena, M. C. Reguera, L. Roncal, Weighted weak type estimates for non-integral square functions, arXiv:2506.14897

  4. M. Fraccaroli, D. Kosz, L. Roncal, On differentiation of integrals in Lebesgue spaces, arXiv:2505.05425

  5. A. Fernández-Bertolin, L. Roncal, D. Stan, Landis-type results for discrete equations, arXiv: 2401.09066

• Published (or accepted for publication)

  1. L. Fanelli, H. Mizutani, L. Roncal, Nico M. Schiavone, Uniform resolvent estimates, smoothing effects and spectral stability for the Heisenberg sublaplacian, arXiv: 2409.11943, to appear in J. Anal. Math.

  2. F. Di Plinio, M. Flórez-Amatriain, I. Parissis, L. Roncal, Pointwise localization and sharp weighted bounds for Rubio de Francia square functions, Publ. Mat. 69 (2025), no. 2, 445-471.

  3. L. Fanelli, H. Mizutani, L. Roncal, Nico M. Schiavone, Non-existence of radial eigenfunctions for the perturbed Heisenberg sublaplacian, J. Fourier Anal. Appl. 31 (2025), Paper No. 37.

  4. H. Gimperlein, B. Krötz, L. Roncal, S. Thangavelu, Poisson transform and unipotent complex geometry, J. Funct. Anal. 288 (2025), no. 3, Paper No. 110742.

  5. O. Bakas, F. Di Plinio, I. Parissis, and L. Roncal, Singular integrals along variable codimension one subspaces, Ars Inven. Anal. 2024, Paper No. 2, 53 pp.

  6. A. Fernández-Bertolin, L. Roncal, A. Rüland, On (global) unique continuation properties of the fractional discrete Laplacian, J. Funct. Anal. 286 (2024), no. 9, Paper No. 110375.

  7. N. Accomazzo, F. Di Plinio, P. Hagelstein, I. Parissis, L. Roncal, Directional square functions, Anal. PDE. 16 (2023), 1651-1699.

  8. A. Nowak, L. Roncal, T.Z. Szarek, Endpoint estimates and optimality for the generalized spherical maximal operator on radial functions, Comm. Pure Appl. Anal. 22 (2023), 2233-2277. 

  9. D. Kosz, G. Rey, L. Roncal, Weak-type maximal function estimates on the infinite-dimensional torus, Math. Z. 304 (2023), 43.

  10. L. Fanelli, L. Roncal, Kato-Ponce estimates for fractional sublaplacians in the Heisenberg group, Bull. Lond. Math. Soc. 55 (2023), 611-639.

  11. D. Kosz, J. Martínez-Perales, V. Paternostro, E. Rela, L. Roncal, Maximal operators on the infinite-dimensional torus, Math. Annalen 385 (2023), 1-39.

  12. L. Roncal, D. Stan, L. Vega, Carleman type inequalities for fractional relativistic operators, Rev. Mat. Complut. 36 (2023), 301-332.

  13. L. Roncal and S. Thangavelu, Corregindum to: An extension problem and trace Hardy inequality for the sublaplacian on $H$-type groups, Int. Math. Res. Not. IMRN 12 (2022), 9598-9602.

  14. D. Beltran, R. Oberlin, L. Roncal, A. Seeger, B. Stovall, Variation bounds for spherical averages, Math. Annalen 382 (2022), no. 1-2, 459-512.

  15. L. Roncal, Hardy type inequalities for the fractional relativistic operator, Math. Eng. 4 (2022), no. 3, Paper No. 18, 16pp.

  16. J. Canto, K. Li, L. Roncal, O. Tapiola, $C_p$ estimates for rough homogeneous singular integrals and sparse forms, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 22 (2021), no.3, 1131-1168.

  17. A. Fernández-Bertolin, L. Roncal, A. Rüland, D. Stan, Discrete Carleman estimates and three balls inequalities, Calc. Var. Partial Differential Equations 60 (2021), no.6, Paper No. 239.

  18. L. Roncal, S. Shrivastava, K. Shuin, Bilinear spherical maximal functions of product type, J. Fourier Anal. Appl. 27 (2021), Paper No. 73.

  19. S. Bagchi, S. Hait, L. Roncal, S. Thangavelu, On the maximal function associated to the spherical means on the Heisenberg group, New York J. Math. 27 (2021), 631-675.

  20. R. Garg, L. Roncal, S. Shrivastava, Quantitative weighted estimates for Rubio de Francia's Littlewood--Paley square function, J. Geom. Anal. 31 (2021), 748-771.

  21. E. Fernández, L. Roncal, A decomposition of Calderón-Zygmund type and some observations on differentiation of integrals on the infinite-dimensional torus, Potential Anal. 53 (2020), 1449-1465.

  22. L. Roncal, S. Thangavelu, An extension problem and trace Hardy inequality for the sublaplacian on $H$-type groups, Int. Math. Res. Not. IMRN 14 (2020), 4238-4294.

  23. Ó. Ciaurri, A. Nowak, L. Roncal, Maximal estimates for a generalized spherical mean Radon transform acting on radial functions, Ann. Mat. Pura Appl. (4) 199 (2020), 1597-1619.

  24. P. Boggarapu,  L. Roncal, S. Thangavelu, On extension problem, trace Hardy and Hardy's inequalities for some fractional Laplacians, Comm. Pure Appl. Anal. 18 (2019), 2575-2605.

  25. K. Li, C. Pérez, I.P. Rivera-Ríos, L. Roncal, Weighted norm inequalities for rough singular integral operators, J. Geom. Anal. 29 (2019), 2526-2564

  26. E. Fernández, L. Roncal, On the absolute divergence of Fourier series in the infinite dimensional torus, Colloq. Math. 157 (2019), 143-155

  27. C. Pérez, I.P. Rivera-Ríos, L. Roncal, $A_1$ theory of weights for rough homogeneous singular integrals and commutators, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 19 (2019), 169-190

  28. Ó. Ciaurri, L. Roncal, S. Thangavelu, Hardy-type inequalities for fractional powers of the Dunkl--Hermite operator, Proc. Edinburgh Math. Soc. (2) 61 (2018), no. 2, 513–544

  29. Ó. Ciaurri, L. Roncal, P. R. Stinga, J.L. Torrea, J.L. Varona, Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications, Adv. Math. 330 (2018), 688-738

  30. C. Lizama, L. Roncal, Hölder-Lebesgue regularity and almost periodicity for  semidiscrete equations with a fractional Laplacian, Discrete Contin. Dyn. Syst. 38 (2018), no.3, 1365-1403

  31. Ó. Ciaurri, L. Roncal, Vector-valued extensions for fractional integrals of Laguerre expansions, Studia Math. 240 (2018), no.1, 69-99

  32. Ó. Ciaurri, A. Nowak, L. Roncal, Two-weight mixed norm estimates for generalized spherical mean Radon transform acting on radial functions, SIAM J. Math. Anal. 49 (2017), no. 6, 4402-4439

  33. P. Boggarapu, L. Roncal, S. Thangavelu,  Mixed norm estimates for the Cesàro means associated with Dunkl--Hermite expansions, Trans. Amer. Math. Soc. 369 (2017), 7021-7047

  34. Ó. Ciaurri, T. A. Gillespie, L. Roncal, J. L. Torrea, J. L. Varona, Harmonic Analysis associated with a discrete Laplacian,  J. Anal. Math. 132 (2017), 109-131

  35. T. P. Hytönen, L. Roncal, O. Tapiola, Quantitative weighted estimates for rough homogeneous singular integrals, Israel J. Math. 218 (2017), 133--164

  36.  Ó. Ciaurri, E. Fernández, L. Roncal,  Revisiting floating bodies, Expo. Math. 34 (2016), 396-422

  37.  L. Roncal, S. Thangavelu, Hardy's inequality for fractional powers of the sublaplacian on the Heisenberg group, Adv. Math. 302 (2016), 106-158

  38. J. Dziubanski, M. Preisner, L. Roncal, P. R. Stinga, Hardy spaces for Fourier-Bessel expansions, J. Anal. Math. 128 (2016), 261-287

  39. L. Roncal, P. R. Stinga, Fractional Laplacian on the torus, Commun. Contemp. Math. 18 (2016) 1550033, 26 pp.

  40.  Ó. Ciaurri, L. Roncal, P. R. Stinga, Riesz transforms on compact Riemannian symmetric spaces of rank one, Milan J. Math. 83 (2015), 345-370

  41. Ó. Ciaurri, C. Lizama, L. Roncal, J. L. Varona, On a connection between the discrete fractional Laplacian and superdiffusion, Appl. Math. Lett. 49 (2015), 119-125

  42. Ó. Ciaurri, L. Roncal, J. L. Varona, The multiplier of the interval $[-1,1]$ for the Dunkl transform of arbitrary order on the real line, Integral Transforms Spec. Funct. 26 (2015), 728-736

  43.  A. Nowak, L. Roncal, Potential operators associated with Jacobi and Fourier-Bessel expansions, J. Math. Anal. Appl. 422 (2015), 148-184

  44. Ó. Ciaurri, L. Roncal, The Riesz transform for the harmonic oscillator in spherical coordinates, Constr. Approx. 40 (2014), 447-472

  45.  A. Nowak and L. Roncal, On sharp heat and subordinated kernel estimates in the Fourier-Bessel setting, Rocky Mountain J. Math. 44 (2014), 1321-1342

  46.  A. Nowak, L. Roncal, Sharp heat kernel estimates in the Fourier-Bessel setting for a continuous range of the type parameter, Acta Math. Sin. 30 (2014), 437-444

  47. Ó. Ciaurri, L. Roncal, The wave equation for the Bessel Laplacian, J. Math. Anal. Appl. 409 (2014), 263-274

  48. Ó. Ciaurri, L. Roncal, P. R. Stinga, Fractional integrals on compact Riemannian symmetric spaces of rank one, Adv. Math. 235 (2013), 627-647

  49. Ó. Ciaurri, L. Roncal, Bochner-Riesz means for Fourier-Bessel expansions: norm inequalities for the maximal operator and almost everywhere convergence, J. Approx. Theory 167 (2013), 121-146

  50.  Ó. Ciaurri, L. Roncal, Higher order Riesz transforms for Fourier-Bessel expansions, J. Fourier Anal. Appl. 18 (2012), 770-789

  51. A. Nowak, L. Roncal, K. Stempak, Riesz transforms for the Dunkl Ornstein-Uhlenbeck semigroup, Colloq. Math. 118 (2010), 669-684

  52.  V. Kolyada, L. Roncal, Jacobi transplantations and Weyl integrals, Collect. Math. 61 (2010), 205-221

  53. Ó. Ciaurri, L. Roncal, Littlewood-Paley-Stein $g_k$-functions for Fourier-Bessel expansions, J. Funct. Anal. 258 (2010), 2173-2204

  54. Ó. Ciaurri, L. Roncal, Weighted inequalities for the Bochner-Riesz means related to the Fourier-Bessel expansions, J. Math. Anal. Appl. 329 (2007), 1170-1180

  55. Ó. Ciaurri, L. Roncal, The Bochner-Riesz means for Fourier-Bessel expansions, J. Funct. Anal. 228 (2005), 89-113

Conference proceedings, book chapters, survey articles

1. A. Fernández-Bertolin, L. Roncal, D. Stan, Landis' conjecture: a survey, arXiv:2412.00788,  to appear in Harmonic Analysis and Nonlinear Partial Differential Equations, RIMS Kôkyûroku Bessatsu, 2025

2. S. Kumar, F. Ponce-Vanegas, L. Roncal, L. Vega, The Frisch-Parisi formalism for fluctuations of the Schrödinger equation, Mathematical Physics and Its Interactions, 199–223, Springer Proc. Math. Stat., 451, Springer, Singapore, 2024 

3.  L. Roncal, Huellas del análisis de Fourier en el Premio Princesa de Asturias de Investigación Científica y Técnica 2020, Gac. R. Soc. Mat. Esp. 24 (2021), 35-54

4. Ó. Ciaurri, L. Roncal, Hardy's inequality for the fractional powers of a discrete Laplacian, J. Anal. 26 (2018), no. 2, 211-225, Proceedings of 20th Ramanujan Symposium International Conference

5. A. Arenas, Ó. Ciaurri, E. Labarga, L. Roncal, J. L. Varona, Series de Fourier no trigonométricas: una perspectiva familiar, Zubía, Monográfico 26 (2014), 39-54

6. L. Roncal, P. R. Stinga, Transference of fractional Laplacian regularity, Special Functions, Partial Differential Equations and Harmonic Analysis. In honor of Calixto P. Calderón, in: Springer Proceedings in Mathematics and Statistics 108, A. M. Stokolos, C. Georgakis, and W. Urbina (Eds.) (2014), 203-212

7. E. Fernández, L. Roncal, Los números de Ramsey y el álgebra, Gac. R. Soc. Mat. Esp. 15 (2012), 651-674

8. Ó. Ciaurri, E. Fernández. R. Larrea, L. Roncal, Vietè's product: a proof in the finest ancient style, College Math. J. 43 (2012), 291-296

9. Ó. Ciaurri, L. Roncal, J.L. Torrea, J.L. Varona, How to define the Riesz transform for Fourier-Neumann expansions?, Contribuciones científicas en honor de Mirian Andrés, Servicio de Publicaciones de la Universidad de La Rioja, ISBN 978-84-96487-50-5, Logroño, La Rioja (2010), 203-215

PhD Thesis

Weighted boundedness of operators related to the Fourier-Bessel expansions (advisor Óscar Ciaurri)