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

PhD Thesis

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

Publications 

• Preprints

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

  2. L. Fanelli, H. Mizutani, L. Roncal, Nico M. Schiavone, Non-existence of radial eigenfunctions for the perturbed Heisenberg sublaplacian, arXiv: 2310.18050

  3. F. Di Plinio, M. Flórez-Amatriain, I. Parissis, L. Roncal, Pointwise localization and sharp weighted bounds for Rubio de Francia square functions, arXiv:2308:01442

  4. H. Gimperlein, B. Krötz, L. Roncal, S. Thangavelu, Poisson transform and unipotent complex geometry, arXiv:2206.14088

• Published (or accepted for publication)

  1. 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.

  2. 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.

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

  4. 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. 

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

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

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

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

  9. 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.

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

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

  12. 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.

  13. 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.

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

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  21. 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

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

  23. 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

  24. 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

  25. 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

  26. 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

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

  28. 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

  29. 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

  30. 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

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

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

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

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

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

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

  37. 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

  38. 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

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

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

  41.  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

  42.  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

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

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

  45. 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

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

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

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

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

  50. 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

  51. 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. 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 

2.  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

3. 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

4. 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

5. 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

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

7. 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

8. 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