$L^T_p-$ functions on locally compact groups

F. Abtahi H. G. Amini; A. Rejali

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arXiv · 2110.06302

$L^T_p-$ functions on locally compact groups

F. Abtahi H. G. Amini·A. Rejali

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Abstract

Let $G$ be a locally compact group and $1\leq p<\infty$. Based on some important earlier works, in this paper the concept of $L_p^T-$function is introduced. Then the structure of the space $L^{T}_p(G)$, which is consisting of all $L_p^T-$functions, is investigated. As an important result, $L^{T}_p(G)^+$ is completely characterized, for the class of amenable locally compact groups. Furthermore, it is verified some applications of Plancherel Theorem on $L^{T}_2(G)$, in the class of abelian locally compact groups.

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BibTeX RIS

F. Abtahi H. G. Amini, A. Rejali. 2021-10-12. $L^T_p-$ functions on locally compact groups. https://arxiv.org/abs/2110.06302

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