Sharp Riesz-Fejér Inequality for Harmonic Hardy Spaces

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 Kayumov et al. (Potential Anal. 52, 105–113, 2020) and resolving the posed conjecture.