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

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

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (1): 81-92.doi: 10.1016/S0252-9602(11)60210-5

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

吕小芬

Department of Mathematics, University of Science and Technology of |China, Hefei 230026, China, Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China|Department of Mathematics, Huzhou Teachers College, |Huzhou 313000, China|Department of Mathematics, Huzhou Teachers College, |Huzhou 313000, China

收稿日期:2007-09-25 修回日期:2009-08-15 出版日期:2011-01-20 发布日期:2011-01-20
基金资助:
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).

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

TANG Xiao-Min, HU Zhang-Jian, LV Xiao-Fen

Department of Mathematics, University of Science and Technology of |China, Hefei 230026, China, Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China|Department of Mathematics, Huzhou Teachers College, |Huzhou 313000, China|Department of Mathematics, Huzhou Teachers College, |Huzhou 313000, China

Received:2007-09-25 Revised:2009-08-15 Online:2011-01-20 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).

摘要/Abstract

摘要：

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.

关键词: Harmonic function, mixed norm space, Bloch-type space, norm, derivatives

Abstract:

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

中图分类号:

31C05

唐笑敏, 胡璋剑, 吕小芬. DERIVATIVES OF HARMONIC MIXED NORM AND BLOCH-TYPE SPACES IN THE UNIT BALL OF Rⁿ[J]. 数学物理学报(英文版), 2011, 31(1): 81-92.

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

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

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