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Bibliographic Details
Main Authors: Nowak, Adam, Sasso, Emanuela, Sjögren, Peter, Stempak, Krzysztof
Format: Preprint
Published: 2022
Subjects:
Online Access:https://arxiv.org/abs/2209.04236
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Table of Contents:
  • We investigate mapping properties of non-centered Hardy-Littlewood maximal operators related to the exponential measure $dμ(x) = \exp(-|x_1|-\ldots-|x_d|)dx$ in $\mathbb{R}^d$. The mean values are taken over Euclidean balls or cubes ($\ell^{\infty}$ balls) or diamonds ($\ell^1$ balls). Assuming that $d \ge 2$, in the cases of cubes and diamonds we prove the $L^p$-boundedness for $p > 1$ and disprove the weak type $(1,1)$ estimate. The same is proved in the case of Euclidean balls, under the restriction $d \le 4$ for the positive part.