A note on characterization of $H^1$ Sobolev spaces by square functions

TL;DR

This paper characterizes $H^1$ Sobolev spaces using specific square functions, providing an improvement over earlier results in the field.

Contribution

It introduces a new characterization of $H^1$ Sobolev spaces through square functions, enhancing the understanding of their structure.

Findings

New square function characterization of $H^1$ Sobolev spaces

Improved results over previous characterizations

Enhanced tools for analysis of Sobolev spaces

Abstract

We establish characterization of $H^1$ Sobolev spaces by certain square functions, improving previous results.