Good Lambda Inequalities and Variable Orlicz Hardy Spaces

TL;DR

This paper establishes a general link between good-$lambda$ inequalities and bounds in variable Orlicz spaces, applying these results to analyze variable Orlicz Hardy spaces within the unit disc.

Contribution

It introduces a general theorem connecting good-$lambda$ inequalities with variable Orlicz space bounds and applies it to Hardy spaces in the unit disc.

Findings

Proves a general theorem linking good-$lambda$ inequalities to variable Orlicz space bounds.

Derives new results on variable Orlicz Hardy spaces in the unit disc.

Abstract

We prove a general theorem showing that local good-$\lambda$ inequalities imply bounds in certain variable Orlicz spaces. We use this to prove results about variable Orlicz Hardy spaces in the unit disc.