Acta mathematica scientia, Series B >
DECOMPOSITION THEOREMS FOR Qp SPACES WITH SMALL SCALE p ON THE UNIT BALL OF Cn
Received date: 2009-02-11
Online 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).
This article is devoted to studying the decomposition of functions of Qp spaces, which unify Bloch space and BMOA space in the scale of p. A decomposition theorem is established for Qp spaces 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 Qp, 0 spaces is given as well.
Key words： Qp spaces; decomposition; Carleson measure
PENG Ru , OUYANG-Cai-Heng . DECOMPOSITION THEOREMS FOR Qp SPACES WITH SMALL SCALE p ON THE UNIT BALL OF Cn[J]. Acta mathematica scientia, Series B, 2010 , 30(5) : 1419 -1428 . DOI: 10.1016/S0252-9602(10)60134-8
[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 Qp 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 Qp spaces 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 Qp 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 Qp Functions. Frontiers in Mathematics. Basel: Birkh\"auser, 2006
[13] Yang W. Carleson type measure characterization of Qp spaces. Analysis, 1998, 18: 345--349
[14] Yang W. Vanishing Carleson type measure characterization of Qp, 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
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