Laurent Moonens

activity

20152023

most citedDifferentiating along rectangles in lacunary directions

2 citations · 2 across the 7 of their papers we have counts for

collaborators

11 papers

math.AP2023

Hausdorff dimension of removable sets for elliptic and canceling homogeneous differential operators in the class of bounded functions

Victor Biliatto, Laurent Moonens, Tiago Picon

In this note we give an upper bound on the Hausdorff dimension of removable setsfor elliptic and canceling homogeneous differential operators with constant coefficients in the clas…

math.CA2022

Almost everywhere convergence for Lebesgue differentiation processes along rectangles

Emma D'Aniello, Anthony Gauvan, Laurent Moonens +1

In this paper, we study Lebesgue differentiation processes along rectangles $R_{k}$ shrinking to the origin in the Euclidean plane, and the question of their almost everywhere conver…

math.CA2022

(Un)boundedness of directional maximal operators through a notion of "Perron capacity'' and an application

Emma D'Aniello, Anthony Gauvan, Laurent Moonens

We introduce the notion of \textit{Perron capacity} of a set of slopes $Ω \subset R$ . Precisely, we prove that if the Perron capacity of $Ω$ is finite then the directional…

math.AP2020

On Local Continuous Solvability of Equations Associated to Elliptic and Canceling Linear Differential Operators

Laurent Moonens, Tiago Picon

Consider $A (x, D) : C^{\infty} (Ω, E) \to C^{\infty} (Ω, F)$ an elliptic and canceling linear differential operator of order $ν$ with smooth complex coefficients in $Ω\subset \mathb…

math.AP2020

Solvability In Weighted Lebesgue Spaces of the Divergence Equation with Measure Data

Laurent Moonens, Emmanuel Russ

In the following paper, one studies, given a bounded, connected open set $Ω$ $\subseteq$ R n , $κ$ > 0, a positive Radon measure $μ$ 0 in $Ω$ and a (signed) Radon measure $μ$ on $Ω…

math.CA2019

Differentiating along rectangles with fixed shapes in a set of directions

Emma D'Aniello, Laurent Moonens

In the present note, we examine the behavior of some homo\-thecy-invariant differentiation basis of rectangles in the plane satisfying the following requirement: for a given rectan…

math.CA2018

Differentiating Orlicz spaces with rare bases of rectangles

Emma D 'Aniello, Laurent Moonens, Joseph Rosenblatt

In the current paper, we study how the speed of convergence of a sequence of angles decreasing to zero influences the possibility of constructing a rare differentiation basis of re…

math.AP2017

Continuous solutions for divergence-type equations associated to elliptic systems of complex vector fields

Laurent Moonens, Tiago Picon

In this paper, we characterize all the distributions $F \in D^{'} (U)$ such that there exists a continuous weak solution $v \in C (U, C^{n})$ (with $U \subset Ω$ ) to t…

math.CA2016

Averaging on $n$ -dimensional rectangles

Emma D'Aniello, Laurent Moonens

In this work we investigate families of translation invariant differentiation bases $B$ of rectangles in $R^{n}$ , for which $L lo g^{n - 1} L (R^{n})$ is the largest Orlicz space that $B$ d…

math.CA2016★ 2 cited

Differentiating along rectangles in lacunary directions

Laurent Moonens

We show that, given some lacunary sequence of angles $θ = (θ_{j})_{j \in N}$ not converging too fast to zero, it is possible to build a rare differentiation basis $B$ o…

math.CA2015

Removable singularities for div v = f in weighted Lebesgue spaces

Laurent Moonens, Emmanuel Russ, Heli Tuominen

Let $w \in L^{1}_l oc (R^{n})$ be apositive weight. Assuming that a doubling condition and an $L^{1}$ Poincaré inequality on balls for the measure $w (x) d x$ , as well as a growth conditio…