The Generalized Grand Wiener Amalgam Spaces and the boundedness of Hardy-Littlewood maximal operators

TL;DR

This paper introduces a new class of generalized grand Wiener amalgam spaces, explores their properties, and analyzes the boundedness of Hardy-Littlewood maximal operators within these spaces.

Contribution

It generalizes previous grand Wiener amalgam spaces using generalized grand Lebesgue spaces and studies the boundedness of maximal operators in this new setting.

Findings

Defined the generalized grand Wiener amalgam spaces.

Established basic properties and embeddings of these spaces.

Analyzed the boundedness of Hardy-Littlewood maximal operators.

Abstract

In \cite{g5}, we defined and investigated the grand Wiener amalgam space $W(L^{p),\theta_1}(\Omega), L^{q),\theta_2}(\Omega))$ , where $1<p,q<\infty, \theta_1>0, \theta_2>0$, $\Omega\subset\mathbb R^{n} $ and the Lebesgue measure of $\Omega$ is finite. In the present paper we generalize this space and define the generalized grand Wiener amalgam space $W(L_{a}^{p)}(\mathbb R^{n}), L_{b}^{q)}(\mathbb R^{n})),$ where $L_{a}^{p)}(\mathbb R^{n})$ and $L_{b}^{q)}(\mathbb R^{n}),$ are the generalized grand Lebesgue spaces, (see \cite{u}, \cite{su3}). Later we investigate some basic properties. Next we study embeddings for these spaces and we discuss boundedness and unboundedness of the Hardy-Littlewood maximal operator between some generalized grand Wiener amalgam spaces.