1. Regularity Techniques for Elliptic PDEs and the Fractional Laplacian. With a foreword by Luis A. Caffarelli and José L. Torrea. Chapman & Hall, CRC Press, 334 pp, 2024. A book preview can be found here.
   

1. Extension problem and Harnack's inequality for some fractional operators, Comm. Partial Differential Equations 35 (2010), 2092--2122 (with J. L. Torrea).
2. Regularity theory for the fractional harmonic oscillator, J. Funct. Anal. 260 (2011), 3097--3131 (with J. L. Torrea).
3. Square functions associated to Schrödinger operators, Studia Math. 203 (2011), 171--194 (with I. Abu-Falahah and J. L. Torrea).
4. Regularity properties of Schrödinger operators, J. Math. Anal. Appl. 388 (2012), 817--837 (with T. Ma, J. L. Torrea and C. Zhang).
5. Fractional integrals on compact Riemannian symmetric spaces of rank one, Adv. Math. 235 (2013), 627--647 (with Ó. Ciaurri and L. Roncal).
6. Harnack's inequalities for fractional nonlocal equations, Discrete Contin. Dyn. Syst. 33 (2013), 3153--3170 (with C. Zhang).
7. A T1 criterion for Hermite-Calderón-Zygmund operators on the BMO_H(R^n) space and applications, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) XII (2013), 157--187 (with  J. J. Betancor, R. Crescimbeni, J. C. Fariña and J. L. Torrea).
8. Rate of convergence of Wong--Zakai approximations for stochastic partial differential equations, Proceedings of the Seventh Seminar on Stochastic Analysis, Random Fields and Applications VII, Ascona 2011, in: Progress in Probability 67, R. Dalang, M. Dozzi and F. Russo (Eds), 95--130, Birkhäuser Basel, 2013 (with I. Gyöngy).
9. Extension problem for fractional operators: semigroups and wave equations, J. Evol. Equ. 13 (2013), 343--368 (with J. E. Galé and P. J. Miana).
10. A note on the almost everywhere convergence to initial data for some evolution equations, Potential Anal. 40 (2014), 195--202 (with I. Abu-Falahah and J. L. Torrea).
11. Regularity estimates in Hölder spaces for Schrödinger operators via a T1 theorem, Ann. Mat. Pura Appl. 193 (2014), 561--589 (with T. Ma, J. L. Torrea and C. Zhang).
12. The fractional Bessel equation in Hölder spaces, J. Approx. Theory 184 (2014), 55--99 (with J. J. Betancor and A. J. Castro).
13. 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 L. Roncal).
14. Fractional semilinear Neumann problems arising from a fractional Keller--Segel model, Calc. Var. Partial Differential Equations 54 (2015), 1009--1042 (with B. Volzone).
15. Riesz transforms on compact Riemannian symmetric spaces of rank one, Milan J. Math. 83 (2015), 345--370 (with Ó. Ciaurri and L. Roncal).
16. Maximum principles, extension problem and inversion for nonlocal one-sided equations, J. Differential Equations 260 (2016), 6333--6362 (with A. Bernardis, F. J. Martín-Reyes and J. L. Torrea).
17. Fractional Laplacian on the torus, Commun. Contemp. Math. 18 (2016), 1550033, 26pp. (with L. Roncal).
18. Hardy spaces for Fourier--Bessel expansions, J. Anal. Math. 128 (2016), 261--287 (with J. Dziubański, M. Preisner and L. Roncal).
19. Fractional elliptic equations, Caccioppoli estimates and regularity, Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), 767--807 (with L. A. Caffarelli).
20. On weighted mixed-norm Sobolev estimates for some basic parabolic equations, Commun. Pure Appl. Anal. 16 (2017), 855--882 (with L. Ping and J. L. Torrea).
21. Harnack inequality for the fractional nonlocal linearized Monge--Ampère equation, Calc. Var. Partial Differential Equations 56 (2017), 56:103 (with D. Maldonado).
22. Regularity theory and extension problem for fractional nonlocal parabolic equations and the master equation, SIAM J. Math. Anal. 49 (2017), 3893--3924 (with J. L. Torrea).
23. Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications, Adv. Math. 330 (2018), 688--738 (with Ó. Ciaurri, L. Roncal, J. L. Torrea and J. L. Varona).
24. The fractional nonlocal Ornstein--Uhlenbeck equation, Gaussian symmetrization and regularity, Discrete Contin. Dyn. Syst. 38 (2018), 3269--3298 (with F. Feo and B. Volzone).
25. Fractional Laplacians on the sphere, the Minakshisundaram zeta function and semigroups, New Developments in the Analysis of Nonlocal Operators, 167--189, Contemp. Math. 723, Amer. Math. Soc., Providence, RI, 2019 (with P. L. De Nápoli).
26. User's guide to the fractional Laplacian and the method of semigroups, Handbook of Fractional Calculus with Applications, Anatoly Kochubei, Yuri Luchko (Eds.), Fractional Differential Equations, 235--266, Berlin, Boston, De Gruyter, 2019.
27. One-sided fractional derivatives, fractional Laplacians and weighted Sobolev spaces, Nonlinear Anal. 193 (2020), 111505 (with M. Vaughan).
28. The obstacle problem for a fractional Monge--Ampère equation, Comm. Partial Differential Equations 45 (2020), 457--482 (with Y. Jhaveri).
29. Hölder, Sobolev, weak-type and BMO estimates in mixed-norm with weights for parabolic equations, Sci. China Math. 64 (2021), 129--154 (with J. L. Torrea).
30. Regularity for C1,α interface transmission problems, Arch. Ration. Mech. Anal. 240 (2021), 265--294 (with L. A. Caffarelli and M. Soria-Carro).
31. Regularity estimates for nonlocal space-time master equations in bounded domains, J. Evol. Equ. 21 (2021), 503--565 (with A. Biswas).
32. Harnack inequalities and Hölder estimates for master equations, SIAM J. Math. Anal. 53 (2021), 2319--2348 (with A. Biswas and M. De León-Contreras).
33. Fractional elliptic equations in nondivergece form: definition, applications and Harnack inequality, J. Math. Pures Appl. 156 (2021), 245--306 (with M. Vaughan).
34. Fractional derivatives: Fourier, elephants, memory effects, viscoelastic materials, and anomalous diffusions, Notices Amer. Math. Soc. 70 (2023), no. 4, 576--587.
35. Regularity of viscosity solutions to fully nonlinear elliptic transmission problems, Adv. Math. 435 (2023), 109353, 52 pp (with M. Soria-Carro).
36. Sharp extension problem characterizations for higher fractional power operators in Banach spaces, J. Funct. Anal. 287 (2024), 110474, 27 pp (with A. Biswas)
37. A PDE approach to the existence and regularity of surfaces of minimum mean curvature variation, Arch. Ration. Mech. Anal. (2024), to appear (with L. A. Caffarelli and H. Vivas).

1. Fractional powers of first order differential operators and new families of polynomials associated to inverse measures, (2022) submitted (with M. Mazzitelli and J. L. Torrea).
2. Interior Schauder estimates for fractional elliptic equations in nondivergence form, (2024) submitted (with M. Vaughan).
   

Video lectures

1. The Signorini problem, fractional Laplacians and the language of semigroups, Newton Institute, Cambridge UK (2014).
   
2. On nonlocal Monge--Ampère equations, ICERM - Brown University (2018).
3. Ecuaciones de Monge--Ampère no locales, Café Matemático - Universidad Nacional de Mar del Plata (2020).
4. Nonlocal fractional Monge--Ampère equations, AIMS-Cameroon Research Centre Colloquium (2021).
5. Regularity for C1,α interface transmission problems, Two Nonlinear Days in Urbino (2021).
6. Harnack inequality for fractional nondivergence form elliptic equations, Virtual Analysis and PDE Seminar (2022).
7. Fractional derivatives: Fourier, elephants, memory effects, viscoelastic materials, and anomalous diffusions, Center for Mathematics and Artificial Intelligence Colloquium (2023).
8. Abel, Caffarelli and fractional nonlocal equations, presentation given at the Evening of the Abel Prize 2023 -- Highlighting the work of Luis Caffarelli, held at the Royal Netherlands Academy of Arts and Sciences (KNAW), Amsterdam (2024).
   

Preprints

1. Fractional discrete Laplacian versus discretized fractional Laplacian, (2015) preprint (with Ó. Ciaurri, L. Roncal, J. L. Torrea and J. L. Varona).
2. Boolos' Hardest Logic Puzzle Ever in its purest form, (2018) preprint (with J. J. Colomina-Almiñana)

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