The dual spaces of variable anisotropic Hardy-Lorentz spaces and continuity of a class of linear operators

TL;DR

This paper investigates the dual spaces of variable anisotropic Hardy-Lorentz spaces and establishes the continuity of certain linear operators, revealing new duality and boundedness results in variable exponent settings.

Contribution

It introduces the dual space characterization of variable anisotropic Hardy-Lorentz spaces as anisotropic BMO-type spaces with variable exponents and proves the continuity of specific linear operators.

Findings

Dual space of variable anisotropic Hardy-Lorentz spaces is anisotropic BMO-type spaces with variable exponents.

Established the boundedness of a class of linear operators on these spaces.

Results are new even for constant exponent cases.

Abstract

In this paper, the author obtain the continuity of a class of linear operators on variable anisotropic Hardy-Lorentz spaces. In addition, the author also obtain that the dual space of variable anisotropic Hardy-Lorentz spaces is the anisotropic BMO-type spaces with variable exponents. This result is still new even when the exponent function $p(\cdot)$ is $p$.