The boundedness of commutators of sublinear operators on Herz Triebel-Lizorkin spaces with variable exponent

TL;DR

This paper investigates the boundedness of commutators of sublinear operators on Herz Triebel-Lizorkin spaces with variable exponents, providing new characterizations and boundedness results for various classical operators.

Contribution

It introduces a new characterization of Herz Triebel-Lizorkin spaces with variable exponents and proves boundedness of Lipschitz commutators of sublinear operators on these spaces.

Findings

Boundedness of commutators of maximal, Riesz potential, and Calderón-Zygmund operators.

Characterization of Herz Triebel-Lizorkin spaces via operator families.

Establishment of boundedness estimates for specific operator commutators.

Abstract

In this paper, the authors first discuss the characterization of Herz Triebel-Lizorkin spaces with variable exponent via two families of operators. By this characterization, the authors prove that the Lipschitz commutators of sublinear operators is bounded from Herz spaces with variable exponent to Herz Triebel-Lizorkin spaces with variable exponent. As an application, the corresponding boundedness estimates for the commutators of maximal operator, Riesz potential operator and Calder\'on-Zygmund operator are established.