Acta mathematica scientia, Series B >
DERIVATIVES OF HARMONIC MIXED NORM AND BLOCH-TYPE SPACES IN THE UNIT BALL OF Rn
Received date: 2007-09-25
Revised date: 2009-08-15
Online published: 2011-01-20
Supported by
Supported by the NNSF of China (10771064, 10971063), the NSF of Zhejiang Province (Y6100219, Y7080197, Y6090036, D7080080), and the Innovation Team Foundation of the Department of Education of Zhejiang Province (T200924).
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 Hp,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 Hp,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
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 . DOI: 10.1016/S0252-9602(11)60210-5
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