$L^T_p-$ functions on locally compact groups

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

$L^T_p-$ functions on locally compact groups

Functional Analysis 2021-10-14 v1

Authors: F. Abtahi H. G. Amini , A. Rejali

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.

Keywords

lp spaces and inequalities local-global principles topological groups

Cite

@article{arxiv.2110.06302,
  title  = {$L^T_p-$ functions on locally compact groups},
  author = {F. Abtahi H. G. Amini and A. Rejali},
  journal= {arXiv preprint arXiv:2110.06302},
  year   = {2021}
}

$L^T_p-$ functions on locally compact groups

Abstract

Keywords

Cite

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