Convolution on L p-spaces of a locally compact group

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 som...

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Bibliographic Details
Published in:Mathematica Slovaca 2013-04, Vol.63 (2), p.291-298
Main Authors: Abtahi, Fatemeh, Nasr-Isfahani, Rasoul, Rejali, Ali
Format: Article
Language:English
Subjects:
convolution
locally compact group
Lp-space
Primary 43A15
Secondary 43A20
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Summary: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.
ISSN:0139-9918
1337-2211
DOI:10.2478/s12175-012-0098-6