DECOMPOSITION THEOREMS FOR Qp SPACES WITH SMALL SCALE p ON THE UNIT BALL OF Cn

doi:10.1016/S0252-9602(10)60134-8

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (5): 1419-1428.doi: 10.1016/S0252-9602(10)60134-8

DECOMPOSITION THEOREMS FOR Q_p SPACES WITH SMALL SCALE p ON THE UNIT BALL OF Cⁿ

彭茹^{1, 2,3}, 欧阳才衡²

1. Department of Mathematics, Wuhan University of Technology, Wuhan 430070, China;
2. Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071, China;
3. Graduate School, The Chinese Academy of Sciences, Beijing 100039, China

收稿日期:2009-02-11 出版日期:2010-09-20 发布日期:2010-09-20
基金资助:
This reseach was supported in part by the NSFC (10971219)and the Fundamental Research Funds for the Central Universityies (2010-Ia-023).

DECOMPOSITION THEOREMS FOR Q_p SPACES WITH SMALL SCALE p ON THE UNIT BALL OF Cⁿ

PENG Ru^{1, 2,3}, OUYANG-Cai-Heng²

1. Department of Mathematics, Wuhan University of Technology, Wuhan 430070, China;
2. Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071, China;
3. Graduate School, The Chinese Academy of Sciences, Beijing 100039, China

Received:2009-02-11 Online:2010-09-20 Published:2010-09-20
Supported by:
This reseach was supported in part by the NSFC (10971219)and the Fundamental Research Funds for the Central Universityies (2010-Ia-023).

摘要/Abstract

摘要：

This article is devoted to studying the decomposition of functions of Q_p spaces, which unify Bloch space and BMOA space in the scale of p. A decomposition theorem is established for Q_pspaces with small scale p, n-1/ n <p ≤1 by means of p-Carleson measure and the Bergman metric on the unit ball of Cⁿ. At the same time, a decomposition theorem for Q_p_{, 0} spaces is given as well.

关键词: Q_p spaces, decomposition, Carleson measure

Abstract:

Key words: Q_p spaces, decomposition, Carleson measure

中图分类号:

32A37

彭茹, 欧阳才衡. DECOMPOSITION THEOREMS FOR Q_p SPACES WITH SMALL SCALE p ON THE UNIT BALL OF Cⁿ[J]. 数学物理学报(英文版), 2010, 30(5): 1419-1428.

PENG Ru, OUYANG-Cai-Heng. DECOMPOSITION THEOREMS FOR Q_p SPACES WITH SMALL SCALE p ON THE UNIT BALL OF Cⁿ[J]. Acta mathematica scientia,Series B, 2010, 30(5): 1419-1428.

参考文献

[1] Aulaskari R, Lappan P. Criteria for analytic functions to be Bloch and a harmonic or meromorphic function to be normal//Yang C C, Wen G C, Li K Y, Chiang Y M, eds. Complex Analysis and its Applications. Pitman Res Notes Math Ser 305. Harlow: Longman Sci Tech, 1994: 136--146

[2] Aulaskari R, Xiao J, Zhao R H. On subspaces and subsets of BMOA and UBC. Analysis, 1995, 15: 101--121

[3] Li B, Ouyang C H. Higher radial derivative of functions of Q_p spaces and its applications. J Math Anal Appl, 2007, 327: 1257--1272

[4] Ouyang C H, Yang W S, Zhao R H. Characterizations of Bergman spaces and Bloch space in the unit ball of Cⁿ. Trans Amer Math Soc, 1995, 347: 4301--4313

[5] Ouyang C H, Yang W S, Zhao R H. M\"obius invariant Q_pspaces associated with the Green's function on the unit ball of Cⁿ. Pacific J Math, 1998, 182: 69--99

[6] Rochberg R. Decomposition theorems for Bergman spaces and their applications//Power S C, eds. Operators and Function Theory,
Dordrecht: Reidel, 1985: 225--278

[7] Rochberg R, Semmes S. A decomposition theorem for BMO and applications. J Funct Anal, 1986, 67: 228--263

[8] Rochberg R, Wu Z. A new characterization of Dirichlet type spaces and applications. Illinois J Math, 1993, 37: 101--122

[9] Rudin W. Function Theory in the Unit Ball of Cⁿ. New York: Springer-Verlag, 1980

[10] Wu Z, Xie C. Decomposition theorems for Q_p spaces. Ark Mat, 2002, 40: 383--401

[11] Xiao J. Holomorphic Q Classes. Lecture Notes in Math, Vol 1767. Berlin, Heidelberg: Springer-Verlag, 2001

[12] Xiao J. Geometric Q_p Functions. Frontiers in Mathematics. Basel: Birkh\"auser, 2006

[13] Yang W. Carleson type measure characterization of Q_pspaces. Analysis, 1998, 18: 345--349

[14] Yang W. Vanishing Carleson type measure characterization of Q_p_{, 0}. C R Math Rep Acad Sci Canada, 1999, 21(1): 1--5

[15] Zhu K H. Spaces of Holomorphic Functions in the Unit Ball. Graduate Texts in Mathematics, Vol 226. New York: Springer-Verlag, 2005

DECOMPOSITION THEOREMS FOR Q_p SPACES WITH SMALL SCALE p ON THE UNIT BALL OF Cⁿ

DECOMPOSITION THEOREMS FOR Q_p SPACES WITH SMALL SCALE p ON THE UNIT BALL OF Cⁿ

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	Nihed TRABELSI. SINGULAR LIMIT SOLUTIONS FOR 2-DIMENSIONAL ELLIPTIC SYSTEM WITH SUB-QUADRTATIC CONVECTION TERM[J]. 数学物理学报(英文版), 2018, 38(4): 1174-1194.
[2]	Kwok-Pun HO. DOOB'S INEQUALITY, BURKHOLDER-GUNDY INEQUALITY AND MARTINGALE TRANSFORMS ON MARTINGALE MORREY SPACES[J]. 数学物理学报(英文版), 2018, 38(1): 93-109.
[3]	Hassan Eltayeb GADAIN. SOLVING COUPLED PSEUDO-PARABOLIC EQUATION USING A MODIFIED DOUBLE LAPLACE DECOMPOSITION METHOD[J]. 数学物理学报(英文版), 2018, 38(1): 333-346.
[4]	王利娟. LARGE TIME BEHAVIOR OF SOLUTIONS TO THE PERTURBED HASEGAWA-MIMA EQUATION[J]. 数学物理学报(英文版), 2017, 37(6): 1775-1790.
[5]	张再云, 黄建华, 孙明保. ALMOST CONSERVATION LAWS AND GLOBAL ROUGH SOLUTIONS OF THE DEFOCUSING NONLINEAR WAVE EQUATION ON R²[J]. 数学物理学报(英文版), 2017, 37(2): 385-394.
[6]	彭茹, 吴悠, 邓方文. CARLESON MEASURES, RIEMANN-STIELTJES OPERATORS AND MULTIPLIERS ON F(p, q, s) SPACES IN THE UNIT BALL OF Cⁿ[J]. 数学物理学报(英文版), 2016, 36(3): 635-654.
[7]	陈宇, 周忆. SIMPLE WAVES OF THE TWO DIMENSIONAL COMPRESSIBLE FULL EULER EQUATIONS[J]. 数学物理学报(英文版), 2015, 35(4): 855-875.
[8]	李浩光. CAUCHY PROBLEM FOR LINEARIZED NON-CUTOFF BOLTZMANN EQUATION WITH DISTRIBUTION INITIAL DATUM[J]. 数学物理学报(英文版), 2015, 35(2): 459-476.
[9]	钱涛, 王晋勋, 杨燕. MATCHING PURSUITS AMONG SHIFTED CAUCHY KERNELS IN HIGHER-DIMENSIONAL SPACES[J]. 数学物理学报(英文版), 2014, 34(3): 660-672.
[10]	张学军, 席利华, 范海霞, 李俊锋. ATOMIC DECOMPOSITION OF μ-BERGMAN SPACE IN Cⁿ[J]. 数学物理学报(英文版), 2014, 34(3): 779-789.
[11]	罗振东, 李宏. A POD REDUCED-ORDER SPDMFE EXTRAPOLATING ALGORITHM FOR HYPERBOLIC EQUATIONS[J]. 数学物理学报(英文版), 2014, 34(3): 872-890.
[12]	彭茹, 欧阳才衡. CARLESON MEASURES FOR BESOV-SOBOLEV SPACES WITH APPLICATIONS IN THE UNIT BALL OF Cⁿ[J]. 数学物理学报(英文版), 2013, 33(5): 1219-1230.
[13]	罗振东, 李磊, 孙萍. A REDUCED-ORDER MFE FORMULATION BASED ON POD METHOD FOR PARABOLIC EQUATIONS[J]. 数学物理学报(英文版), 2013, 33(5): 1471-1484.
[14]	李宏, 罗振东, 高骏强. A NEW REDUCED-ORDER FVE ALGORITHM BASED ON POD METHOD FOR VISCOELASTIC EQUATIONS[J]. 数学物理学报(英文版), 2013, 33(4): 1076-1098.
[15]	王海兵, 刘继军. ON DECOMPOSITION METHOD FOR ACOUSTIC WAVE SCATTERING BY MULTIPLE OBSTACLES[J]. 数学物理学报(英文版), 2013, 33(1): 1-22.