Anthony Gauvan

activity

20222025

collaborators

10 papers

math.FA2025

Operator capacity, the Brascamp--Lieb inequality and geometric programming

Neal Bez, Anthony Gauvan, Hiroshi Tsuji

The capacity of completely positive operators and the Brascamp--Lieb constant can both be interpreted in terms of unconstrained geometric programming up to an additional minimisati…

math.CA2024

A note on ubiquity of geometric Brascamp-Lieb data

Neal Bez, Anthony Gauvan, Hiroshi Tsuji

Relying substantially on work of Garg, Gurvits, Oliveira and Wigderson, it is shown that geometric Brascamp--Lieb data are, in a certain sense, ubiquitous. This addresses a questio…

math.FA2023

Perron's capacity of random sets

Anthony Gauvan

Given a sequence of random variables ${X_{k} : k \geq 1}$ uniformly distributed in $(0, 1)$ and independent, we consider the following random sets of directions $$Ω_{\te…

math.CA2023

Maximal operators on hyperbolic triangles

Anthony Gauvan, Samuel Bronstein, Romain Branchereau

We characterize the boundedness properties on the spaces $L^{p} (H^{2})$ of the maximal operator $M_{B}$ where $B$ is an arbitrary family of hyperbolic triang…

math.CA2023

Sharp weak-type estimate for maximal operators associated to Cartesian families under an arithmetic condition

Anthony Gauvan

Given a set of integers $A \subset Z$ , we consider the smallest family $B_{A^{n - 1}}$ invariant by translation which contains the rectangles $$ R_{\boldsymbol{a}}…

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( $λ$ …