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arXiv · 1709.00380

Weights of reasonable growth and their application

Mateusz Krukowski
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Abstract

In the paper, we introduce the concept of weight with reasonable growth on a locally compact group $G$. We verify that these weights form a natural class to work with, by examining the most common examples. We proceed with the discussion of the $L^p-$conjecture. With the use of Riesz-Thorin-Stein-Weiss interpolation, we establish that \mbox{$L^p_ω(G)\star L^p_ω(G)\subset L^p_ω(G)$}, $p>1$ implies that $L^p_ω(G)\star L^q_ω(G)\subset L^q_ω(G)$ for $q$ which lies between $p$ and $p'$. At last, we confirm the $L^p_ω-$conjecture for weights of $(p,q)-$reasonable growth.

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Mateusz Krukowski. 2018-08-08. Weights of reasonable growth and their application. https://arxiv.org/abs/1709.00380

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