Convolution on L p -spaces of a locally compact group |
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Authors: | Fatemeh Abtahi Rasoul Nasr-Isfahani Ali Rejali |
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Affiliation: | 198. Department of Mathematics, University of Isfahan, Isfahan, Iran 298. Department of Mathematical sciences, Isfahan University of Technology, 84156-83111, Isfahan, Iran
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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. |
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