×

Convolution on \(L^p\)-spaces of a locally compact group. (English) Zbl 1324.43002

Summary: We have recently shown that, for \(2<p<\infty \), a locally compact group \(G\) is compact if and only if the convolution multiplication \(f*g\) exists for all \(f,g\in L^p(G)\). Here, we study the existence of \(f*g\) for all \(f,g\in L^p(G)\) in the case where \(0<p\leq 2\). Also, for \(0<p<\infty \), we offer some necessary and sufficient conditions for \(L^p(G)*L^p(G)\) to be contained in certain function spaces on \(G\).

MSC:

43A15 \(L^p\)-spaces and other function spaces on groups, semigroups, etc.
PDFBibTeX XMLCite
Full Text: DOI

References:

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.