Algebraic property of weighted Lebesgue spaces on a class of hypergroups

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.