Function Theory in Real Hardy Spaces

TL;DR

This paper explores how classical Hardy space results extend to real Hardy spaces, where Fourier coefficients are restricted to real values, revealing exact analogues of known theorems.

Contribution

It establishes that many classical Hardy space theorems have precise counterparts in the setting of real Hardy spaces.

Findings

Classical Hardy space results have exact analogues in real Hardy spaces.

Fourier coefficient restrictions to real values preserve key properties.

Theoretical framework for real Hardy space analysis is developed.

Abstract

We show that many classical results in Hardy space theory have exact analogues when the Fourier coefficients are allowed only to be real.