New characterization of Hardy-Fofana spaces and temperature equation

TL;DR

This paper characterizes Hardy-Fofana spaces using Riesz transforms and describes their elements as bounded solutions to a generalized temperature equation related to the Cauchy-Riemann system.

Contribution

It provides a new characterization of Hardy-Fofana spaces through Riesz transforms and links these spaces to solutions of a temperature equation.

Findings

Hardy-Fofana spaces characterized via Riesz transforms

Distributions in these spaces are bounded solutions to a temperature equation

Establishes a connection between function spaces and PDE solutions

Abstract

The aim of this paper is to give a characterization of Hardy-Fofana spaces via Riesz trasforms. This characterization allow us to describ the distributions belonging to these spaces as a bounded solutions of Cauchy-Riemann's general temperature equations.