Continuous embeddings in harmonic mixed norm spaces on the unit ball in ℝ n

Abstract

In this paper continuous embeddings in spaces of harmonic functions with mixed norm on the unit ball in ℝ n are established, generalizing some Hardy-Littlewood embeddings for similar spaces of holomorphic functions in the unit disc. Differences in indices between the spaces of harmonic and holomorphic spaces are revealed. As a consequence an analogue of classical Fejer-Riesz inequality is obtained. Embeddings in the special case of Riesz systems are also established.