Porosity of certain subsets of Lebesgue spaces on locally compact groups

Authors

  • I. Akbarbaglu University of Zanjan
  • S. Maghsoudi University of Zanjan

Keywords:

Lebesgue space, $\sigma$-$c$-lower porous set, locally compact group, convolution

Abstract

Let $G$ be a locally compact group. In this paper, we show that if $G$ is a non-discrete locally compact group, $p\in(0,1)$ and $q\in(0,+\infty]$, then the set of all pairs $(f, g)\in L^p(G)\times L^q(G)$ for which $f\ast g$ is finite, forms a set of first category in $L^p(G)\times L^q(G)$. 10.1017/S0004972712000949

Author Biography

I. Akbarbaglu, University of Zanjan

Department of Mathematics

Published

2013-07-23

Issue

Vol. 88 No. 1 (2013)

Section

Articles
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