On Hardy spaces of local and nonlocal operators

TL;DR

This paper characterizes Hardy spaces associated with local and nonlocal operators like the Laplacian and fractional Laplacian using Hardy-Stein identities, providing a new analytical framework.

Contribution

It introduces a novel characterization of Hardy spaces for both local and nonlocal operators via Hardy-Stein identities, expanding the understanding of these function spaces.

Findings

Characterization of Hardy spaces for Laplacian and fractional Laplacian

Use of Hardy-Stein identities for space characterization

Framework applicable to local and nonlocal operators

Abstract

We characterize conditional Hardy spaces of the Laplacian and of the fractional Laplacian by using Hardy-Stein type identities.