Sharp constant problems for harmonic mappings

Abstract

The primary objective of this paper is to investigate sharp constant problems in harmonic Hardy spaces. We first establish a sharp asymptotic constant for a Littlewood-Paley type inequality applicable to weak harmonic $(K,K_0)$-quasiregular mappings, where $K\ge 1$ and $K_0\ge 0$. Subsequently, we derive sharp Hardy-Littlewood type constants for harmonic mappings.

arXiv commentThis paper was submitted to a juornal in June 2026