**Research interests**

- Harmonic Analysis: Orthogonal expansions, singular integrals, commutators, weighted estimates, sparse operators, summability methods, Hardy spaces, discrete harmonic analysis, Dunkl theory, abstract harmonic analysis, Heisenberg group.
- Special functions: Bessel functions, Laguerre, Hermite, Jacobi polynomials and functions.
- Partial Differential Equations: wave equation, nonlocal equations, fractional Laplacian, extension problem, regularity, Harnack inequality, Hardy inequality, trace Hardy inequality.
- Geometric Analysis: operators on compact Riemannian manifolds.

**Publications**

Note that some papers can have an appearance and a format different to the used in the corresponding journal. Also, perhaps the final version in the journal will have some other minor changes.

Some of my coauthors have their own webpages:
Jacek Dziubański,
T. Alastair Gillespie,
Tuomas P. Hytönen,
Viktor I. Kolyada,
Kangwei Li,
Carlos Lizama,
Adam Nowak,
Carlos Pérez,
Marcin Preisner,
Israel P. Rivera-Ríos,
Krzysztof Stempak,
Pablo Raúl Stinga,
O. Tapiola,
Sundaram Thangavelu,
José Luis Torrea,
Juan Luis Varona.

- Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications, to appear in Adv. Math., arxiv:1608.08913 (with Ó. Ciaurri, P. R. Stinga, J. L. Torrea, and J. L. Varona); pdf
- A
_{1}theory of weights for rough homogeneous singular integrals and commutators, to appear in Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), arxiv:1607.06432 (with C. Pérez and I. P. Rivera-Ríos); pdf - Hardy-type inequalities for fractional powers of the Dunkl-Hermite operator, to appear in Proc. Edinburgh Math. Soc. (2), arxiv:1602.04997 (with Ó. Ciaurri and S. Thangavelu); pdf
- Hölder-Lebesgue regularity and almost periodicity for semidiscrete equations with a fractional Laplacian, Discrete Continuous Dyn. Syst. 38 (2018), no.3, 1365-1403, (with C. Lizama); pdf.
- Vector-valued extensions for fractional integrals of Laguerre expansions, Studia Math., 240 (2018), no.1, 69-99, (with Ó. Ciaurri); pdf
- 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, (with Ó. Ciaurri and A. Nowak); pdf.
- Mixed norm estimates for the Cesàro means associated with Dunkl-Hermite expansions, Trans. Amer. Math. Soc. 369 (2017), 7021-7047, (with P. Boggarapu and S. Thangavelu); pdf
- Harmonic Analysis associated with a discrete Laplacian, J. Anal. Math. 132 (2017), 109-131, (with Ó. Ciaurri, T. A. Gillespie, J. L. Torrea, and J. L. Varona); pdf
- Quantitative weighted estimates for rough homogeneous singular integrals, Israel J. Math. 218 (2017), 133-164, (with T. P. Hytönen and O. Tapiola); pdf
- Revisiting floating bodies, Expo. Math. 34 (2016), 396-422, (with Ó. Ciaurri and E. Fernández); pdf
- Hardy's inequality for fractional powers of the sublaplacian on the Heisenberg group, Adv. Math. 302 (2016), 106-158, (with S. Thangavelu); pdf
- Hardy spaces for Fourier-Bessel expansions, J. Anal. Math. 128 (2016), 261-287, (with J. Dziubański, M. Preisner, and P. R. Stinga); pdf
- Fractional Laplacian on the torus, Commun. Contemp. Math. 18 (2016), 1550033, 26 pp. (with P. R. Stinga); pdf
- Riesz transforms on compact Riemannian symmetric spaces of rank one, Milan J. Math. 83 (2015), 345-370 (with Ó. Ciaurri and P. R. Stinga); pdf
- On a connection between the discrete fractional Laplacian and superdiffusion, Appl. Math. Lett. 49 (2015), 119-125, (with Ó. Ciaurri, C. Lizama, and J. L. Varona); pdf
- 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, (with Ó. Ciaurri and J. L. Varona); pdf
- Potential operators associated with Jacobi and Fourier-Bessel expansions, J. Math. Anal. Appl. 422 (2015), 148-184, (with A. Nowak); pdf
- On sharp heat and subordinated kernel estimates in the Fourier-Bessel setting, Rocky Mountain J. Math. 44 (2014), 1321-1342; (with A. Nowak); pdf
- The Riesz transform for the harmonic oscillator in spherical coordinates, Constr. Approx. 40 (2014), 447-472, (with Ó. Ciaurri); pdf
- Sharp heat kernel estimates in the Fourier-Bessel setting for a continuous range of the type parameter, Acta Math. Sin. 30 (2014), 437-444, (with A. Nowak); pdf
- The wave equation for the Bessel Laplacian, J. Math. Anal. Appl. 409 (2014), 263-274, (with Ó. Ciaurri); pdf
- Fractional integrals on compact Riemannian symmetric spaces of rank one, Adv. Math. 235 (2013), 627-647; (with Ó. Ciaurri and P. R. Stinga); pdf
- Bochner-Riesz means for Fourier-Bessel expansions: norm inequalities for the maximal operator and almost everywhere convergence, J. Approx. Theory 167 (2013), 121-146, (with Ó. Ciaurri); pdf
- Higher order Riesz transforms for Fourier-Bessel expansions, J. Fourier Anal. Appl. 18 (2012), 770-789, (with Ó. Ciaurri); pdf
- Jacobi transplantations and Weyl integrals, Collect. Math. 61 (2010), 205-221, (with V. Kolyada); pdf
- Riesz transforms for the Dunkl Ornstein-Uhlenbeck semigroup, Colloq. Math. 118 (2010), 669-684 (with A. Nowak and K. Stempak); pdf
- Littlewood-Paley-Stein
g
_{k}-functions for Fourier-Bessel expansions, J. Funct. Anal. 258 (2010), 2173-2204, (with Ó. Ciaurri); pdf - Weighted inequalities for the Bochner-Riesz means related to the Fourier-Bessel expansions, J. Math. Anal. Appl. 329 (2007), 1170-1180, (with Ó. Ciaurri); pdf
- The Bochner-Riesz means for Fourier-Bessel expansions, J. Funct. Anal. 228 (2005), 89-113, (with Ó. Ciaurri); pdf

**Preprints submitted for publication**

- A decomposition of Calderón--Zygmund type and some observations on differentiation of integrals on the infinite-dimensional torus, pdf (con E. Fernández).
- On the absolute divergence of Fourier series in the infinite dimensional torus, pdf (with E. Fernández).
- An extension problem and trace Hardy inequality for the sublaplacian on H-type groups, arxiv:1708.09258 (with S. Thangavelu).
- On extension problem, trace Hardy and Hardy's inequalities for some fractional Laplacians, pdf (with P. Boggarapu and S. Thangavelu).
- Weighted norm inequalities for rough singular integral operators, arxiv:1701.05170 (with K. Li, C. Pérez, and I. P. Rivera-Ríos).

**Preprints not submitted for publication**

- Fractional discrete Laplacian versus discretized fractional Laplacian, arxiv:1507.04986 (with Ó. Ciaurri, P. R. Stinga, J. L. Torrea y J. L. Varona).

**Conference proceedings, book chapters, survey articles**

- Hardy's inequality for the fractional powers of a discrete Laplacian, to appear in J. Anal., proceedings of 20th Ramanujan Symposium International Conference (with Ó. Ciaurri); pdf
- Series de Fourier no trigonométricas: una perspectiva familiar, Zubía, Monográfico 26 (2014), 39-54, (with A. Arenas, Ó. Ciaurri, E. Labarga y J. L. Varona); pdf
- 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 (with P. R. Stinga); pdf
- Los números de Ramsey y el álgebra, Gac. R. Soc. Mat. Esp. 15 (2012), 651-674, (with E. Fernández); pdf
- Vietè's product: a proof in the finest ancient style, College Math. J. 43 (2012), 291-296, (with Ó. Ciaurri, E. Fernández and R. Larrea); pdf
- 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, Logroño, La Rioja (2010), 203-215, (with Ó. Ciaurri, J. L. Torrea, and J. L. Varona); pdf

**Ph. D. Thesis**

Here is my PhD Thesis.