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

doi:10.1016/S0252-9602(11)60210-5

Abstract

Abstract:

Let H(B) be the set of all harmonic functions f on the unit ball B of Rⁿ. 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.

Key words: Harmonic function, mixed norm space, Bloch-type space, norm, derivatives

CLC Number:

31C05

TANG Xiao-Min, HU Zhang-Jian, LV Xiao-Fen. DERIVATIVES OF HARMONIC MIXED NORM AND BLOCH-TYPE SPACES IN THE UNIT BALL OF Rⁿ[J].Acta mathematica scientia,Series B, 2011, 31(1): 81-92.

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

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