Convolution on L p-spaces of a locally compact group

Author:

Abtahi Fatemeh1,Nasr-Isfahani Rasoul2,Rejali Ali1

Affiliation:

1. Department of Mathematics, University of Isfahan, Isfahan, Iran

2. Department of Mathematical sciences, Isfahan University of Technology, 84156-83111, Isfahan, Iran

Abstract

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

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Amenability and Super-amenability of Some Feichtinger Algebras;Iranian Journal of Science and Technology, Transactions A: Science;2020-07-02

2. The amalgam space L(p,q)π$\begin{array}{} L^{\pi}_{(p,q)} \end{array}$(G) on IN-groups;Mathematica Slovaca;2020-02-25

3. Dichotomies for Orlicz spaces;Mathematica Slovaca;2016-02-01

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