### Recent Submissions

• #### 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\, ...
• #### 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 ...
• #### Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation ﻿

(2018-07-06)
We give the asymptotics of the Fourier transform of self-similar solutions to the modified Korteweg-de Vries equation, through a fixed point argument in weighted $W^{1,\infty}$ around a carefully chosen, two term ansatz. ...
• #### On the improvement of the Hardy inequality due to singular magnetic fields ﻿

(2018-07-12)
We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type ...
• #### Regularity of fractional maximal functions through Fourier multipliers ﻿

(2018)
We prove endpoint bounds for derivatives of fractional maximal functions with either smooth convolution kernel or lacunary set of radii in dimensions $n \geq 2$. We also show that the spherical fractional maximal function ...
• #### Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds ﻿

(2018)
The sharp Wolff-type decoupling estimates of Bourgain--Demeter are extended to the variable coefficient setting. These results are applied to obtain new sharp local smoothing estimates for wave equations on compact Riemannian ...
• #### Sparse bounds for pseudodifferential operators ﻿

(Journal d'Analyse Mathématique, 2018)
We prove sparse bounds for pseudodifferential operators associated to H\"ormander symbol classes. Our sparse bounds are sharp up to the endpoint and rely on a single scale analysis. As a consequence, we deduce a range of ...
• #### Spectral stability of Schrödinger operators with subordinated complex potentials ﻿

(Journal of Spectral Theory, 2018-06-28)
We prove that the spectrum of Schroedinger operators in three dimensions is purely continuous and coincides with the non-negative semiaxis for all potentials satisfying a form-subordinate smallness condition. By developing ...
• #### On the Relationship between the One-Corner Problem and the $M-$Corner Problem for the Vortex Filament Equation ﻿

(Journal of Nonlinear Science, 2018-06-28)
In this paper, we give evidence that the evolution of the vortex filament equation (VFE) for a regular M-corner polygon as initial datum can be explained at infinitesimal times as the superposition of M one-corner initial ...
• #### Sharp exponential localization for eigenfunctions of the Dirac Operator ﻿

(2018)
We determine the fastest possible rate of exponential decay at infinity for eigenfunctions of the Dirac operator $\mathcal D_n + \mathbb V$, being $\mathcal D_n$ the massless Dirac operator in dimensions $n=2,3$ and ...
• #### 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 ...
• #### Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials ﻿

(Letters in Mathematical Physics, 2018)
We describe the self-adjoint realizations of the operator $H:=-i\alpha\cdot \nabla + m\beta + \mathbb V(x)$, for $m\in\mathbb R$, and $\mathbb V(x)= |x|^{-1} ( \nu \mathbb{I}_4 +\mu \beta -i \lambda \alpha\cdot{x}/{|x|}\,\beta)$, ...
• #### 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 ...
• #### Variable Lorentz estimate for nonlinear elliptic equations with partially regular nonlinearities ﻿

(Nonlinear Analysis, 2018-02-15)
We prove global Calder\'on-Zygmund type estimate in Lorentz spaces for variable power of the gradients to weak solution of nonlinear elliptic equations in a non-smooth domain. We mainly assume that the nonlinearities are ...
• #### Zero limit of entropic relaxation time for the Shliomis model of ferrofluids ﻿

(2018-02-11)
We construct solutions for the Shilomis model of ferrofluids in a critical space, uniformly in the entropic relaxation time $\tau \in (0, \tau_0)$. This allows us to study the convergence when $\tau\to 0$ for such solutions.
• #### Lorentz estimates for the gradient of weak solutions to elliptic obstacle problems with partially BMO coefficients ﻿

(Boundary Value Problems, 2017)
We prove global Lorentz estimates for variable power of the gradient of weak solution to linear elliptic obstacle problems with small partially BMO coefficients over a bounded nonsmooth domain. Here, we assume that the ...