Analysis of Partial Differential Equations (APDE)
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SPECTRAL ASYMPTOTICS FOR $\delta$INTERACTIONS ON SHARP CONES
(Journal of Mathematical Analysis and Applications, 2017)We investigate the spectrum of threedimensional Schr\"odinger operators with $\delta$interactions of constant strength supported on circular cones. As shown in earlier works, such operators have infinitely many eigenvalues ... 
Weighted mixed weaktype 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 DunklHermite 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 DunklHermite expansions on $\mathbb{R}^d$. These expansions arise when one considers the DunklHermite operator ... 
Dispersive effects of weakly compressible and fast rotating inviscid fluids
(Discrete and Continuous Dynamical Systems  Series A, 201708)We consider a system describing the motion of an isentropic, inviscid, weakly compressible, fast rotating fluid in the whole space $\mathbb{R}^3$, with initial data belonging to $ H^s \left( \mathbb{R}^3 \right), s>5/2 $. ... 
On pointwise and weighted estimates for commutators of CalderónZygmund operators
(Advances in Mathematics, 2017)In recent years, it has been well understood that a CalderónZygmund operator T is pointwise controlled by a finite number of dyadic operators of a very simple structure (called the sparse operators). We obtain a similar ... 
Weak and strong $A_p$$A_\infty$ estimates for square functions and related operators
(Proceedings of the American Mathematical Society, 201707)We prove sharp weak and strong type weighted estimates for a class of dyadic operators that includes majorants of both standard singular integrals and square functions. Our main new result is the optimal bound $[w]_{A_p} ... 
The relativistic spherical $\delta$shell interaction in $\mathbb{R}^3$: spectrum and approximation
(Journal of Mathematical Physics, 20170803)This note revolves on the free Dirac operator in $\mathbb{R}^3$ and its $\delta$shell interaction with electrostatic potentials supported on a sphere. On one hand, we characterize the eigenstates of those couplings by ... 
Highly rotating fluids with vertical stratification for periodic data and vanishing vertical viscosity
(Revista Matemática Iberoamericana, 201707)We prove that the threedimensional, periodic primitive equations with zero vertical diffusivity are globally well posed if the Rossby and Froude number are sufficiently small. The initial data is considered to be of zero ... 
Sharp weighted estimates involving one supremum
(Comptes Rendus Mathematique, 201707)In this note, we study the sharp weighted estimate involving one supremum. In particular, we give a positive answer to an open question raised by Lerner and Moen. We also extend the result to rough homogeneous singular ... 
Derivation of limit equation for a singular perturbation of a 3D periodic Boussinesq system
(Discrete and Continuous Dynamical Systems  Series A, 20170715)We consider a system describing the dynamics of an hydrodynamical, densitydependent flow under the effects of gravitational forces. We prove that if the Froude number is sufficiently small such system is globally well ... 
Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications
(Mathematical Inequalities & Applications, 20170718)Let $I_{v}\left( x\right) $ be modified Bessel functions of the first kind. We prove the monotonicity property of the function $x\mapsto I_{u}\left( x\right) I_{v}\left( x\right) /I_{\left( u+v\right) /2}\left( x\right) ... 
HartreeFock theory with a selfgenerated magnetic field
(Journal of Mathematical Physics, 20170601)We prove the existence of a ground state within the HartreeFock theory for atoms and molecules, in the presence of selfgenerated magnetic fields, with and without direct spin coupling. The ground state exists provided ... 
Sharp bounds for the ratio of modified Bessel functions
(Mediterranean Journal of Mathematics, 20170621)Let $I_{\nu }\left( x\right) $ be the modified Bessel functions of the first kind of order $\nu $, and $S_{p,\nu }\left( x\right) =W_{\nu }\left( x\right) ^{2}2pW_{\nu }\left( x\right) x^{2}$ with $W_{\nu }\left( x\right) ... 
Lorentz estimates for asymptotically regular fully nonlinear parabolic equations
(Mathematische Nachrichten, 20170620)We prove a global Lorentz estimate of the Hessian of strong solutions to the CauchyDirichlet problem for a class of fully nonlinear parabolic equations with asymptotically regular nonlinearity over a bounded $C^{1,1}$ ... 
Some remarks on the $L^p$ regularity of second derivatives of solutions to nondivergence elliptic equations and the Dini condition
(Rendiconti Lincei  Matematica e Applicazioni, 20170530)In this note we prove an endpoint regularity result on the $L^P$ integrability of the second derivatives of solutions to nondivergence form uniformly elliptic equations whose second derivatives are a priori only known ... 
Gaussian Decay of Harmonic Oscillators and related models
(Journal of Mathematical Analysis and Applications, 20170515)We prove that the decay of the eigenfunctions of harmonic oscillators, uniform electric or magnetic fields is not stable under 0order complex perturbations, even if bounded, of these Hamiltonians, in the sense that we can ... 
An efficient multigrid strategy for largescale molecular mechanics optimization
(Journal of Computational Physics, 20170801)Static mechanical properties of materials require largescale nonlinear optimization of the molecular mechanics model under various controls. This paper presents an efficient multigrid strategy to solve such problems. This ... 
A quantitative approach to weighted Carleson condition
(Concrete Operators, 20170505)Quantitative versions of weighted estimates obtained by F. Ruiz and J.L. Torrea for the operator \[ \mathcal{M}f(x,t)=\sup_{x\in Q,\,l(Q)\geq t}\frac{1}{Q}\int_{Q}f(x)dx \qquad x\in\mathbb{R}^{n}, \, t \geq0 \] are ... 
Sparse domination theorem for multilinear singular integral operators with $L^{r}$Hörmander condition
(Michigan Mathematical Journal, 20170401)In this note, we show that if $T$ is a multilinear singular integral operator associated with a kernel satisfies the socalled multilinear $L^{r}$Hörmander condition, then $T$ can be dominated by multilinear sparse operators. 
A characterization of two weight norm inequality for LittlewoodPaley $g_{\lambda}^{*}$function
(Journal of Geometric Analysis, 2017)Let $n\ge 2$ and $g_{\lambda}^{*}$ be the wellknown high dimensional LittlewoodPaley function which was defined and studied by E. M. Stein, $$g_{\lambda}^{*}(f)(x)=\bigg(\iint_{\mathbb R^{n+1}_{+}} \Big(\frac{t}{t+xy ...