Derivatives of harmonic mixed norm and bloch-type spaces in the unit ball of R n

Abstract

Let H( B) be the set of all harmonic functions f on the unit ball B of R n. For 0< p,q≤∞ and a normal weight ϕ, the mixed norm space H p , q, ϕ( B) consists of all functions f in H( B) for which the mixed norm ‖·‖ p,q,ϕ < ∞. In this article, we obtain some characterizations in terms of radial, tangential, and partial derivative norms in H p, q, ϕ( B). The parallel results for the Bloch-type space are also obtained. As an application, the analogous problems for polyharmonic functions are discussed.