Weighted Norm Inequalities for Parametric Littlewood-Paley Operators

TL;DR

This paper proves the boundedness of parametric Littlewood-Paley operators between Musielak-Orlicz Hardy and space, including at critical indices, extending classical results in harmonic analysis.

Contribution

It introduces new boundedness results for parametric Littlewood-Paley operators on Musielak-Orlicz spaces, even at critical indices, generalizing classical Hardy space theory.

Findings

Boundedness from Musielak-Orlicz Hardy space to Musielak-Orlicz space

Boundedness to weak Musielak-Orlicz space at critical index

Partially new results for classical Hardy spaces

Abstract

In this paper, the author establishes the boundedness of parametric Littlewood-Paley operators from Musielak-Orlicz Hardy space to Musielak-Orlicz space, or to weak Musielak-Orlicz space at the critical index. Part of these results are new even for classical Hardy space of Fefferman and Stein.