Good Lambda Inequalities and Musielak-Orlicz Hardy Spaces

We prove a general theorem showing that local good-lambda\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document} inequalities imply bounds in certain variable Orlicz spaces. We use this to prove results about variable Orlicz Hardy spaces (also called Musielak-Orlicz Hardy spaces) in the unit disc.