Variable exponent Triebel-Lizorkin-Morrey spaces

TL;DR

This paper introduces variable exponent Morreyfied Triebel-Lizorkin spaces, establishing key inequalities and characterizations that extend classical function space theory to variable exponent settings.

Contribution

It develops the first variable exponent versions of Morreyfied Triebel-Lizorkin spaces and proves a convolution inequality replacing the Hardy-Littlewood maximal inequality.

Findings

Established a convolution inequality for variable exponent spaces

Characterized the new spaces via Peetre maximal functions

Proved the independence of the spaces from the choice of admissible system

Abstract

We introduce variable exponent versions of Morreyfied Triebel-Lizorkin spaces. To that end, we prove an important convolution inequality which is a replacement for the Hardy-Littlewood maximal inequality in the fully variable setting. Using it we obtain characterizations by means of Peetre maximal functions and use them to show the independence of the introduced spaces from the admissible system used.