### Envíos recientes

• #### Two-weight mixed norm estimates for a generalized spherical mean Radon transform acting on radial functions ﻿

(SIAM Journal on Mathematical Analysis, 2018)
We investigate a generalized spherical means operator, viz. generalized spherical mean Radon transform, acting on radial functions. We establish an integral representation of this operator and find precise estimates of ...
• #### Vector-valued extensions for fractional integrals of Laguerre expansions ﻿

(Studia Math., 2018)
We prove some vector-valued inequalities for fractional integrals defined for several orthonormal systems of Laguerre functions. On the one hand, we obtain weighted $L^p-L^q$ vector-valued extensions, in a multidimensional ...
• #### Hölder-Lebesgue regularity and almost periodicity for semidiscrete equations with a fractional Laplacian ﻿

(Discrete Contin. Dyn. Syst., 2018)
We study the equations $\partial_t u(t,n) = L u(t,n) + f(u(t,n),n); \partial_t u(t,n) = iL u(t,n) + f(u(t,n),n)$ and $\partial_{tt} u(t,n) =Lu(t,n) + f(u(t,n),n)$, where $n\in \mathbb{Z}$, $t\in (0,\infty)$, and $L$ ...
• #### Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications ﻿

The analysis of nonlocal discrete equations driven by fractional powers of the discrete Laplacian on a mesh of size $h>0$ $(-\Delta_h)^su=f,$ for $u,f:\Z_h\to\R$, $0<s<1$, is performed. The pointwise nonlocal ...
• #### Hardy-type inequalities for fractional powers of the Dunkl-Hermite operator ﻿

(Proc. Edinburgh Math. Soc. (2), 2018)
We prove Hardy-type inequalities for a fractional Dunkl–Hermite operator, which incidentally gives Hardy inequalities for the fractional harmonic oscillator as well. The idea is to use h-harmonic expansions to reduce the ...
• #### A Global well-posedness result for the Rosensweig system of ferrofluids ﻿

(Rev. Mat. Iberoam., 2019)
In this Paper we study a Bloch-Torrey regularization of the Rosensweig system for ferrofluids. The scope of this paper is twofold. First of all, we investigate the existence and uniqueness of Leray-Hopf solutions of this ...
• #### Vector-valued operators, optimal weighted estimates and the $C_p$ condition ﻿

(Science China Mathematics, 2018-09)
In this paper some new results concerning the $C_p$ classes introduced by Muckenhoupt and later extended by Sawyer, are provided. In particular we extend the result to the full range expected $p>0$, to the weak norm, to ...
• #### Asymptotic behaviour of neuron population models structured by elapsed-time ﻿

(Nonlinearity, 2019-01-04)
We study two population models describing the dynamics of interacting neurons, initially proposed by Pakdaman et al (2010 Nonlinearity 23 55–75) and Pakdaman et al (2014 J. Math. Neurosci. 4 1–26). In the first model, the ...
• #### El efecto de Talbot: de la óptica a la ecuación de Schrödinger ﻿

(TEMat, 2017-07)
El objetivo de este artículo es dar a conocer un bello efecto óptico que se denomina efecto de Talbot. Primero, describiremos el fenómeno y comentaremos su descubrimiento a mediados del siglo XIX. A continuación, analizaremos ...
• #### Robust numerical methods for nonlocal (and local) equations of porous medium type. Part II: Schemes and experiments ﻿

(SIAM Journal on Numerical Analysis, 2018)
• #### On the global well-posedness of a class of 2D solutions for the Rosensweig system of ferrofluids ﻿

(Journal of Differential Equations, 2018-09)
We study a class of 2D solutions of a Bloch-Torrey regularization of the Rosensweig system in the whole space, which arise when the initial data and the external magnetic field are 2D. We prove that such solutions are ...
• #### Weighted norm inequalities for rough singular integral operators ﻿

(Journal of Geometric Analysis, 2018-08-17)
In this paper we provide weighted estimates for rough operators, including rough homogeneous singular integrals $T_\Omega$ with $\Omega\in L^\infty(\mathbb{S}^{n-1})$ and the Bochner--Riesz multiplier at the critical index ...
• #### Defects in Nematic Shells: a Gamma-convergence discrete-to-continuum approach ﻿

(Archive for Rational Mechanics and Analysis, 2018-07)
In this paper we rigorously investigate the emergence of defects on Nematic Shells with a genus different from one. This phenomenon is related to a non-trivial interplay between the topology of the shell and the alignment ...
• #### On the regularity of solutions to the k-generalized korteweg-de vries equation ﻿

(Proceedings of the American Mathematical Society, 2018-07)
This work is concerned with special regularity properties of solutions to the k-generalized Korteweg-de Vries equation. In [Comm. Partial Differential Equations 40 (2015), 1336–1364] it was established that if the initial ...
• #### Absence of eigenvalues of two-dimensional magnetic Schroedinger operators ﻿

(2018-01-01)
By developing the method of multipliers, we establish sufficient conditions on the electric potential and magnetic field which guarantee that the corresponding two-dimensional Schroedinger operator possesses no point ...