An intrinsic square function on weighted Herz spaces with variable exponent

TL;DR

This paper introduces a new class of weighted Herz spaces with variable exponents and proves the boundedness of an intrinsic square function on these spaces, expanding the understanding of harmonic analysis in variable exponent settings.

Contribution

It defines generalized Herz spaces with weights and variable exponents and establishes the boundedness of an intrinsic square function on these spaces.

Findings

Boundedness of intrinsic square function on weighted Herz spaces with variable exponents.

Conditions on exponents and weights for boundedness.

Extension of harmonic analysis tools to variable exponent spaces.

Abstract

We define new generalized Herz spaces having weight and variable exponent, that is, weighted Herz spaces with variable exponent. We prove the boundedness of an intrinsic square function on those spaces under proper assumptions on each exponent and weight.