Sharp Riesz-Fejér inequality for harmonic Hardy spaces

Abstract

We prove sharp version of Riesz-Fejér inequality for functions in harmonic Hardy space $h^p(\mathbb{D})$ on the unit disk $\mathbb{D}$, for $p>1,$ thus extending the result from \cite{KPK} and resolving the posed conjecture.

5 pages; this version has been accepted for publication in Potential Analysis