On the Lp-conjecture for locally compact groups |
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Authors: | F. Abtahi R. Nasr-Isfahani A. Rejali |
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Affiliation: | (1) Department of Mathematics, University of Isfahan, Isfahan, Iran;(2) Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran |
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Abstract: | Let G be a locally compact group. For 1 < p < ∞, it is well-known that f * g exists and belongs to Lp(G) for all f, g Lp (G) if and only if G is compact. Here, for 2 < p < ∞, we show that f * g exists for all f, g Lp(G) if and only if G is compact. We also show that this result does not remain true for 1 < p ≤ 2. Received: 23 April 2006 |
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Keywords: | Primary: 43A15 Secondary: 43A20 |
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