DERIVATIVES OF HARMONIC MIXED NORM AND BLOCH-TYPE SPACES IN THE UNIT BALL OF Rn

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