Algebraic property of weighted Lebesgue spaces on a class of hypergroups

Tabatabaie, Seyyed Mohammad; Bagheri Salec, AliReza; AlBehadili, Naeem Mankhi Oudah

doi:10.22060/ajmc.2025.23979.1345

Algebraic property of weighted Lebesgue spaces on a class of hypergroups

Articles in Press

Document Type : Original Article

Authors

Seyyed Mohammad Tabatabaie ¹

AliReza Bagheri Salec ¹

Naeem Mankhi Oudah AlBehadili ¹^{, 2}

¹ Department of Mathematics, University of Qom, Qom, Iran

² Accounting Technologies Department, Technical Institute of AMARA, Southern Technical University, Basrah, Iraq

10.22060/ajmc.2025.23979.1345

Abstract

In this paper, in the context of an important class of locally compact hypergroups, namely $\mathcal{K}_{\rho}$, which were introduced by Dunkl and Ramirez, we find some sufficient conditions on a weight $(w_n)_{n=0}^\infty\subseteq (0,\infty)$ such that the set
\begin{equation*}
\left\{\big((f_k)_k,(g_k)_k\big)\in L^p(\mathcal{K}_{\rho})\times L^q(\mathcal{K}_{\rho}):\sum_{k=1}^\infty |f_kg_k|w_k^2\,\rho ^{k-1}<\infty\right\}
\end{equation*}
is a $\sigma$-$c$-lower porous set.

Keywords

Locally compact hypergroups

$\sigma$-lower porous sets

Convolution

Weighted Lebesgue space

Convolution algebra

Subjects