Presentation Abstract
Fame 2026 ConferenceOrlicz Amalgam Spaces as Banach Algebras
Abstract
Let $G$ be a locally compact group, $\Phi_1, \Phi_2$ be Young functions and $\omega$ be a moderate weight function on $G$.
We introduce the weighted Orlicz amalgam space $W(L^{\Phi_1} (G), L_{\omega}^{\Phi_2} (G))$ defined on $G$, whose local component is the Orlicz space $L^{\Phi_1}(G)$ and the global component is the weighted Orlicz space $L_{\omega}^{\Phi_2}(G)$.
We establishes conditions under which this Orlicz amalgam space becomes a Banach algebra with respect to convolution.
We further prove that the Orlicz amalgam algebra $W(L^{\Phi_1} (G), L_{\omega}^{\Phi_2} (G))$ admits no
bounded left approximate identity whenever $G$ is nondiscrete group and that the algebra possesses an identity element if and only if $G$ is discrete.
Our results extend the theory of classical Lebesgue amalgam spaces and convolution Banach algebras to the setting of weighted Orlicz amalgam algebras.
Joint work with Büşra Arıs.