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空间和Bloch空间之间的叠加算子��

作者:未知

  摘 要:设是一个整函数,f为解析函数,由�加盏嫉牡�加算子S���级ㄒ逦�S����(f)=��(f)。对算子S���嫉挠薪缧越�行了研究,给出了叠加算子S���冀�Q��K空间映入��Bloch空间或者将Bloch��空间映入Q��K空间的一个充分必要条件。�И�
  关键词:Bloch空间;��Q��K��空间;叠加算子��
  中图分类号:O174文献标识码:A
  [WT]文章编号:1672-1098(2011)02-0038-03�おおお�
  收稿日期:2011-01-10��
  作者简介:周继振(1976-),男,安徽肥西人,讲师,在读博士,主要从事函数空间和算子理论的研究。��
  
  [WT3BZ]Superposition Operators between��Q��K��and Bloch Space��
  ZHOU Ji-zhen��
  (School of Sciences, Anhui University of Science and Technology, Huainan Anhui 232001, China)��
  Abstract:Let���吉�be an entire function. A superposition operator��S���吉�induced by���吉�, defined by ��S���迹�f)=��(f)��. The author study the boundedness of superposition operator in the paper. A sufficient and necessary condition is given for the superposition operator between ��Q��K��and the Bloch space.��
  Key words:Bloch space;��Q��K��spaces; superposition operator�お�
  
  
  根据文献[5]����209��的引理2, 可构造出一个具有如下性质的域Ω:��
  1) Ω是单连通的;��
  2) Ω保存着无限折线��L=∪∞n=1[w����n-1��,w��n],其中[w����n-1��,w��n]表示连接w����n-1��和w��n�У南叨危华�
  3) 若��f是一个将D�П浠坏溅傅�Riemann映射,则��f∈B�В华�
  4) 对于任意一个��L上的点w�В�其到Ω边界的距离dist(��w,�氮Е�)=��δ��。��
  假设��f是一个将D��变换到Ω的Riemann映射且满足��f(0)=0。 因为f是B空间里的一个单叶函数, 运用文献[
  注释若��K满足条件式(3), 则Q��K是B�У恼孀蛹�,见文献[1]����1 238��的定理2��3。�お�
  参考文献:�お�
  [1] ESSEN M, WULAN H. On analytic and meromorphic functions and spaces of ��Q��K��type[J].Illinois J. Math., 2002, 46:1 233-1 258.��
  [2] ESSEN M, WULAN H, XIAO J. Several function-theoretic characterizations of Mobius invariant ��Q��K��spaces[J]. J. Funct. Anal., 2006, 230: 78-115.��
  [3] XIAO J. Geometric ��Q��p��functions[M]. Basel-Boston-Berlin, Birkhauser Verlag, 2006:25.��
  [4] XIAO J. Holomorphic ��Q��Classes[M].Berlin, Springer LNM, 2001.��
  [5] ALVAREZ V, MARQUEZ M, VUKOTIC D. Superposition operation between the Bloch space and Bergman space[J]. Ark. Mat. 2004, 42:205-216.��
  [6] CAMERA G, GIMENEZ J. The nonliner superoposition operators acting on Bergman space[J].Compos. Math., 1994, 93:23-35.��
  [7] XIONG C. Superposition operators between ��Q��p�� and Bloch-type spaces[J]. Complex. Var, 2005, 50: 935-938.��
  [8] XU W. Superposition operators on Bloch-type space[J]. Comput. Methods Funct. Theory,2007,7:501-507.��
  [9] GIRLA D, MARQUEZ M.Superposition operators between ��Q��p��spaces and Hardy sapces[J]. J. Math. Anal. Appl, 2010, 364:463-472.��
  [10] WULAN H. Criteria for an analytic function to belong to the ��Q��K��spaces[J].Acta.Math.Sci.,2009,29:33-44.��
  [11] POMMERENKE CH. Boundary behaviour of conformal maps[M].Grundlehren Math. Wiss, 299, Berlin, Spring-verlag, 1992:17.��
  [12] LOU Z.Composition operators on Bloch type spaces[J].Analysis,2003,23:81-95.�お�
  (责任编辑:何学华)


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