Riesz-Fejér Inequalities for Harmonic Functions

Abstract

© 2018, Springer Nature B.V. In this article, we prove the Riesz - Fejér inequality for complex-valued harmonic functions in the harmonic Hardy space hp for all p > 1. The result is sharp for p ∈ (1,2]. Moreover, we prove two variant forms of Riesz-Fejér inequality for harmonic functions, for the special case p = 2.