The Smoothness of kernel in Hardy spaces

TL;DR

This paper investigates the properties of kernels in Hardy spaces, demonstrating that these spaces can be characterized using a fixed Lipschitz function, thus advancing the understanding of their structure.

Contribution

It introduces a new characterization of Hardy spaces via a fixed Lipschitz function, extending previous work by G. Weiss.

Findings

Hardy spaces $H^p(\,mathbb{R}^n)$ characterized by Lipschitz functions

Extension of Weiss's results on Hardy spaces

New insights into the structure of Hardy spaces

Abstract

This paper provides a study of problems related to Hardy spaces left by G.\,Weiss in \cite{We}. First, We will prove that the Hardy spaces $H^p(\mathbb{R}^n)$ can be characterized by a fixed Lipschitz function.