### Recent Submissions

• #### 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 ...
• #### Weghted Lorentz and Lorentz-Morrey estimates to viscosity solutions of fully nonlinear elliptic equations ﻿

(Complex Variables and Elliptic Equations, 2018)
We prove a global weighted Lorentz and Lorentz-Morrey estimates of the viscosity solutions to the Dirichlet problem for fully nonlinear elliptic equation $F(D^{2}u,x)=f(x)$ defined in a bounded $C^{1,1}$ domain. The ...
• #### 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 ...
• #### Singular Perturbation of the Dirac Hamiltonian ﻿

(2017-12-15)
This thesis is devoted to the study of the Dirac Hamiltonian perturbed by delta-type potentials and Coulomb-type potentials. We analysed the delta-shell interaction on bounded and smooth domains and its approximation by ...
• #### 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 ...
• #### On a hyperbolic system arising in liquid crystal modelling ﻿

(Journal of Hyperbolic Differential Equations, 2017-11)
We consider a model of liquid crystals, based on a nonlinear hyperbolic system of differential equations, that represents an inviscid version of the model proposed by Qian and Sheng. A new concept of dissipative solution ...
• #### Sphere-valued harmonic maps with surface energy and the K13 problem ﻿

(Advances in the Calculus of Variations, 2017-11)
We consider an energy functional motivated by the celebrated K13 problem in the Oseen-Frank theory of nematic liquid crystals. It is defined for sphere-valued functions and appears as the usual Dirichlet energy with an ...
• #### Global well-posedness and twist-wave solutions for the inertial Qian-Sheng model of liquid crystals ﻿

(Journal of Differential Equations, 2017-10-02)
We consider the inertial Qian-Sheng model of liquid crystals which couples a hyperbolic-type equation involving a second-order material derivative with a forced incompressible Navier-Stokes system. We study the energy law ...
• #### Klein's Paradox and the Relativistic $\delta$-shell Interaction in $\mathbb{R}^3$ ﻿

(Analysis & PDE, 2017-11)
Under certain hypothesis of smallness of the regular potential $\mathbf{V}$, we prove that the Dirac operator in $\mathbb{R}^3$ coupled with a suitable re-scaling of $\mathbf{V}$, converges in the strong resolvent sense ...