Embeddings of harmonic mixed norm spaces on smoothly bounded domains in ℝⁿ

Abstract

The main result of this paper is the embedding (equation presented) 0 < r ≤ r1 ≤ ∞, 0 < s ≤ s1 ≤ ∞, β > -1, of harmonic functions mixed norm spaces on a smoothly bounded domain ω ⊂ ℝn. We also extend a result on boundedness, in mixed norm, of a maximal function-type operator from the case of the unit disc and the unit ball to general domains in ℝn