Variable Fofana's Spaces and their Pre-dual
Fan Yang, Jiang Zhou

TL;DR
This paper introduces variable Fofana's spaces, explores their properties, establishes their pre-dual, and applies these results to characterize fractional integral operators and commutators, extending classical results.
Contribution
It defines variable Fofana's spaces, proves their pre-dual, and applies these findings to fractional integral operators, providing new insights even for classical spaces.
Findings
Established the pre-dual of variable Fofana's spaces.
Characterized fractional integral operators on these spaces.
Extended classical results to variable exponent settings.
Abstract
In this paper, we introduce the variable Fofana's spaces where and , then show some properties and establish the pre-dual of those spaces which are contributed to prove the necessary conditions of fractional integral commutators' boundedness. As applications, the characterization of fractional integral operators and commutators on variable Fofana's spaces are discussed, which are new result even for the classical Fofana's spaces.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Fixed Point Theorems Analysis · Nonlinear Differential Equations Analysis
