Department: Mathematics

Position: Assistant Professor

Degree:

Office: 7.216

Email: alejandro.castilla@nu.edu.kz

Phone: +7 (7172) 709098

Website: https://sites.google.com/site/ajcastroajcastro/home

Position: Assistant Professor

Degree:

Office: 7.216

Email: alejandro.castilla@nu.edu.kz

Phone: +7 (7172) 709098

Website: https://sites.google.com/site/ajcastroajcastro/home

Alejandro joined NU as an Assistant Professor in the Department of Mathematics the summer of 2016. He is from Tenerife (Spain) where he obtained the PhD degree in Mathematics in 2014 at the University of La Laguna. Later he spent two years in Sweden with a PostDoc position at Uppsala University. His research spans a broad area within Harmonic Analysis and its applications to Partial Differential Equations. In particular he has been interested in singular operators associated with orthogonal systems (Bessel, Hermite, Jacobi, Laguerre, etc) and on the well-posedness (i.e. existence and uniqueness of solutions) of low regularity parabolic boundary value problems. Currently he is working on the initial data problem for the Schrödinger equation.

Personal Webpage:** **https://sites.google.com/site/

**SELECTED PUBLICATIONS**

J. Castro, M. Strömqvist, *Homogenization of a a parabolic Dirichlet problem by a method of Dahlberg*, to appear in Publ. Mat. (arXiv:1612.07420).

J. Castro, J.G. Llorente, A. Nicolau, *Oscillation of generalized differences of Hölder and Zygmund functions*, to appear in J. Geom. Anal. (DOI 10.1007/s12220-017-9882-4)

J. Castro, S. Rodríguez-López, W. Staubach, *L^2-solvability of the Dirichlet, Neumann and the regularity problems for parabolic equations with time-independent Hölder-continuous coefficients*, to appear in Trans. Amer. Math. Soc. (https://doi.org/10.1090/tran/6958)

J. Castro, K. Nyström, O. Sande, *Boundedness of single layer potentials associated to divergence form parabolic equations with complex coefficients*, Calc. Var. Partial Differ. Equ. 55 (2016), 1-49.

J. Castro, A. Nowak, T. Z. Szarek, *Riesz-Jacobi transforms as principal value integrals*, Fourier Anal. Appl. 22 (2016), 493-541.

J. Castro, T. Hytönen, *Bounds for partial derivatives: necessity of UMD and sharp constants*, Math. Z. 282 (2016), 635-650.

J. Betancor, A.J. Castro, P.R. Stinga, *The fractional Bessel equation in Hölder spaces*, Approx. Theory 184 (2014), 55-99.

J. Castro, T. Z. Szarek, *On fundamental harmonic analysis operators in certain Dunkl and Bessel settings*, Math. Anal. Appl. 412 (2014), 943-963.

J. Betancor, A.J. Castro, P.L. De Nápoli, J.C. Fariña, L. Rodríguez-Mesa, *Weak type (1,1) estimates for Caffarelli-Calderón generalized maximal operators for semigroups associated with Bessel and Laguerre operators*, Proc. Amer. Math. Soc. 142 (2014), 251-261.

J. Betancor, A.J. Castro, J. Curbelo, J.C. Fariña, L. Rodríguez-Mesa, gamma-radonifying operators and UMD-valued Littlewood-Paley-Stein functions in the Hermite setting on BMO and Hardy spaces, J. Funct. Anal. 263 (2012), 3804-3856.