The weak type $(1,p)$ for convolution operators on locally compact groups

Duván Cardona

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arXiv · 1803.02413

The weak type $(1,p)$ for convolution operators on locally compact groups

Duván Cardona

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Abstract

In this paper we provide necessary and sufficient conditions for the $\textnormal{weak}(1,p)$ boundedness, $1< p<\infty,$ of convolution operators on locally compact (Hausdorff) topological groups. So, we generalize a classical result due to Sobolev-Hardy-Littlewood and Stepanov. Applications to Fourier multipliers on Lie groups also are given.

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BibTeX RIS

Duván Cardona. 2018-03-06. The weak type $(1,p)$ for convolution operators on locally compact groups. https://arxiv.org/abs/1803.02413

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