### Recent Submissions

• #### Unique determination of the electric potential in the presence of a fixed magnetic potential in the plane ﻿

(2018-12)
For electric and magnetic potentials with compact support, we consider the magnetic Schrödinger equation with fixed positive energy. Under a mild additional regularity hypothesis, and with fixed magnetic potential, we show ...
• #### Determination of convection terms and quasi-linearities appearing in diffusion equations ﻿

(2018-12)
We consider the highly nonlinear and ill posed inverse problem of determining some general expression appearing in the a diffusion equation from measurements of solutions on the lateral boundary. We consider both linear ...
• #### Correlation imaging in inverse scattering is tomography on probability distributions ﻿

(Inverse Problems, 2018-12-04)
Scattering from a non-smooth random field on the time domain is studied for plane waves that propagate simultaneously through the potential in variable angles. We first derive sufficient conditions for stochastic moments ...
• #### 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 ...
• #### 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 ...
• #### Proof of an extension of E. Sawyer's conjecture about weighted mixed weak-type estimates ﻿

(Mathematische Annalen, 2018-09)
We show that if $v\in A_\infty$ and $u\in A_1$, then there is a constant $c$ depending on the $A_1$ constant of $u$ and the $A_{\infty}$ constant of $v$ such that \Big\|\frac{ T(fv)} {v}\Big\|_{L^{1,\infty}(uv)}\le c\, ...
• #### 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 ...
• #### On Bloom type estimates for iterated commutators of fractional integrals ﻿

(Indiana University Mathematics Journal, 2018-04)
In this paper we provide quantitative Bloom type estimates for iterated commutators of fractional integrals improving and extending results from [15]. We give new proofs for those inequalities relying upon a new sparse ...
• #### Quantitative weighted estimates for singular integrals and commutators ﻿

(2018-02-27)
In this dissertation several quantitative weighted estimates for singular integral op- erators, commutators and some vector valued extensions are obtained. In particular strong and weak type $(p, p)$ estimates, Coifman-Fe ...
• #### Bilinear representation theorem ﻿

(Transactions of the American Mathematical Society, 2018-01-01)
We represent a general bilinear Calderón--Zygmund operator as a sum of simple dyadic operators. The appearing dyadic operators also admit a simple proof of a sparse bound. In particular, the representation implies a so ...
• #### Improved A1 − A∞ and related estimates for commutators of rough singular integrals ﻿

(Proceedings of the Edinburgh Mathematical Society, 2017)
An $A_1-A_\infty$ estimate improving a previous result in [22] for $[b, T_\Omega]$ with $\Omega\in L^\infty(S^{n-1})$ and $b\in BMO$ is obtained. Also a new result in terms of the $A_\infty$ constant and the one ...
• #### Weighted mixed weak-type inequalities for multilinear operators ﻿

(Studia Mathematica, 2017)
In this paper we present a theorem that generalizes Sawyer's classic result about mixed weighted inequalities to the multilinear context. Let $\vec{w}=(w_1,...,w_m)$ and $\nu = w_1^\frac{1}{m}...w_m^\frac{1}{m}$, the main ...
• #### Mixed norm estimates for the Cesàro means associated with Dunkl-Hermite expansions ﻿

(Transactions of the American Mathematical Society, 2017)
Our main goal in this article is to study mixed norm estimates for the Cesàro means associated with Dunkl--Hermite expansions on $\mathbb{R}^d$. These expansions arise when one considers the Dunkl--Hermite operator ...