Analysis of Partial Differential Equations (APDE)
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Control of pseudodifferential operators by maximal functions via weighted inequalities
(20190101)We establish general weighted L 2 inequalities for pseudodifferential operators associated to the Hörmander symbol classes S ρ,δm . Such inequalities allow one to control these operators by fractional “nontangential” ... 
Subdyadic square functions and applications to weighted harmonic analysis
(20170205)Through the study of novel variants of the classical Littlewood–Paley–Stein gfunctions, we obtain pointwise estimates for broad classes of highlysingular Fourier multipliers on Rd satisfying regularity hypotheses adapted ... 
A FeffermanStein inequality for the Carleson operator
(20180101)We provide a FeffermanStein type weighted inequality for maximally modulated CalderónZygmund operators that satisfy a priori weak type unweighted estimates. This inequality corresponds to a maximally modulated version ... 
Walter Rudin meets Elias M. Stein
(2023)Walter Rudin and Elias M. Stein were giants in the world of mathemat ics. They were loved and admired from students and researchers to teachers and academics, both young and old. They touched many of us through ... 
On the doubling condition in the infinitedimensional setting
(202312)We present a systematic approach to the problem whether a topologically infinitedimensional space can be made homogeneous in the Coifman–Weiss sense. The answer to the question is negative, as expected. Our leading ... 
Sharp estimates for Jacobi heat kernels in conic domains
(2023)We prove genuinely sharp estimates for the Jacobi heat kernels introduced in the context of the multidimensional cone $\mathbb V^{d+1}$and its surface $\mathbb V^{d+1}_0$. To do so, we combine the theory of Jacobi polynomials ... 
Sharp constants in inequalities admitting the Calderón transference principle
(2023)The aim of this note is twofold. First, we prove an abstract version of the Calderón transference principle for inequalities of admissible type in the general commutative multilinear and multiparameter setting. Such an ... 
Boundedness properties of maximal operators on Lorentz spaces
(2023)We study mapping properties of the centered HardyLittlewood maximal operator $\mathcal M$ acting on Lorentz spaces. Given $p \in (1,\infty)$ and a metric measure space $\mathcal X = (X, \rho, \mu)$ we let $\Omega^p_{\rm ... 
Uniform maximal Fourier restriction for convex curves
(2024)We extend the estimates for maximal Fourier restriction operators proved by M\"{u}ller, Ricci, and Wright in \cite{MR3960255} and Ramos in \cite{MR4055940} to the case of arbitrary convex curves in the plane, with constants ... 
Wellposedness of the Kolmogorov twoequation model of turbulence in optimal Sobolev spaces
(20231023)In this paper, we study the wellposedness of the Kolmogorov twoequation model of turbulence in a periodic domain Td, for space dimensions d = 2,3. We admit the average turbulent kinetic energy k to vanish in part of the ... 
Fast rotating nonhomogeneous fluids in thin domains and the Ekman pumping effect
(20231003)In this paper, we perform the fast rotation limit ε → 0+ of the densitydependent incompressible NavierStokes Coriolis system in a thin strip Ωε := R2×] − lε,lε[, where ε ∈]0,1] is the size of the Rossby number and lε > ... 
Weaktype maximal function estimates on the infinitedimensional torus
(202307)We prove necessary and sufficient conditions for the weak $L^p$ boundedness, for $p\in (1,\infty)$, of a maximal operator on the infinitedimensional torus. In the endpoint case $p=1$ we obtain the same weaktype inequality ... 
Weighted BMO estimates for singular integrals and endpoint extrapolation in Banach function spaces
(20230501)In this paper we prove sharp weighted BMO estimates for singular integrals, and we show how such estimates can be extrapolated to Banach function spaces. 
Weighted Lorentz spaces: Sharp mixed A<inf>p</inf> − A<inf>∞</inf> estimate for maximal functions
(20230315)We prove the sharp mixed Ap−A∞ weighted estimate for the HardyLittlewood maximal function in the context of weighted Lorentz spaces, namely [Formula presented] where [Formula presented]. Our method is rearrangement free ... 
Extrapolation in general quasiBanach function spaces
(20231115)In this work we prove offdiagonal, limited range, multilinear, vectorvalued, and twoweight versions of the Rubio de Francia extrapolation theorem in general quasiBanach function spaces. We prove mapping properties of ... 
ALMOST SURE POINTWISE CONVERGENCE OF THE CUBIC NONLINEAR SCHRODINGER EQUATION ON ̈ T 2
(2022)We revisit a result from “Pointwise convergence of the Schr ̈odinger flow, E. Compaan, R. Luc`a, G. Staffilani, International Mathematics Research Notices, 2021 (1), 596647” regarding the pointwise convergence of ... 
Effective surface energies in nematic liquid crystals as homogenised rugosity effects
(2021)We study the effect of boundary rugosity in nematic liquid crystalline systems. We consider a highly general formulation of the problem, able to simultaneously deal with several liquid crystal theories. We use techniques ... 
On C0 and C1 continuity of envelopes of rotational solids and its application to 5axis CNC machining
(202310)We study the smoothness of envelopes generated by motions of rotational rigid bodies in the context of 5axis Computer Numerically Controlled (CNC) machining. A moving cutting tool, conceptualized as a rotational solid, ... 
Lattice points problem, equidistribution and ergodic theorems for certain arithmetic spheres
(20230101)We establish an asymptotic formula for the number of lattice points in the sets Sh1,h2,h3(λ):={x∈Z+3:⌊h1(x1)⌋+⌊h2(x2)⌋+⌊h3(x3)⌋=λ} with λ∈Z+; where functions h1, h2, h3 are constant multiples of regularly varying functions ... 
On the advectiondiffusion equation with rough coefficients: Weak solutions and vanishing viscosity
(20221101)We deal with the vanishing viscosity scheme for the transport/continuity equation ∂tu+div(ub)=0 drifted by a divergencefree vector field b. Under general Sobolev assumptions on b, we show the convergence of such scheme ...