Abstract
Let G be a locally compact abelian group and let M(G) be the measure algebra of G. Assume that μ∈M(G) is power bounded, that is, supn≥0‖μn‖1<∞. This paper is concerned mainly with finding necessary and sufficient conditions for strong convergence of iterates of the convolution operators Tμf:=μ⁎f in Lp(G)(1≤p<∞) spaces. Some related problems are also discussed.
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