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arXiv · 2209.04236

On non-centered maximal operators related to a non-doubling and non-radial exponential measure

Adam Nowak·Emanuela Sasso·Peter Sjögren·Krzysztof Stempak
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Abstract

We investigate mapping properties of non-centered Hardy-Littlewood maximal operators related to the exponential measure $d\mu(x) = \exp(-|x_1|-\ldots-|x_d|)dx$ 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.

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Adam Nowak, Emanuela Sasso, Peter Sjögren, Krzysztof Stempak. 2022-09-09. On non-centered maximal operators related to a non-doubling and non-radial exponential measure. https://doi.org/10.1007/s00208-023-02595-w

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