Anthony Gauvan

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20222025

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5 papers · 1 filter

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.CA2022

Application of Perron Trees to Geometric Maximal Operators

Anthony Gauvan

We characterize the $L^{p} (R^{2})$ boundeness of the geometric maximal operator $M_{a, b}$ associated to the basis $B_{a, b}$ ( $a, b > 0$ ) which is composed of rectangl…

math.CA2022

Restricting directions for Kakeya sets

Anthony Gauvan

We prove that the Kakeya maximal conjecture is equivalent to the $Ω$ -Kakeya maximal conjecture. This completes a recent result in [2] where Keleti and Math{é} proved that the Kakey…

math.CA2022

Kakeya-type sets for Geometric Maximal Operators

Anthony Gauvan

Given a family G of rectangles, to which one associates a tree [G], one defines a natural number $λ$ [G] called its analytic split and satisfying, for all 1 < p < $\infty$ log( $λ$ …