Vector valued inequalities and Littlewood-Paley operators on Hardy spaces

TL;DR

This paper establishes vector valued inequalities linked to Littlewood-Paley theory on Euclidean spaces, aiding the characterization of Hardy spaces through these operators using real analysis techniques.

Contribution

It introduces new vector valued inequalities that facilitate the characterization of Hardy spaces via Littlewood-Paley operators.

Findings

Proved vector valued inequalities for Littlewood-Paley theory.

Applied inequalities to characterize Hardy spaces.

Enhanced understanding of Hardy space characterization methods.

Abstract

We prove certain vector valued inequalities related to Littlewood-Paley theory on Euclidean spaces. They can be used in proving characterization of the Hardy spaces in terms of Littlewood-Paley operators by methods of real analysis.