Generalized Cesàro Operator on Dirichlet Spaces
加权Dirichlet空间上的一般Cesàro算子(英文)
摘要
In this paper, we study the boundedness of the generalized Cesàro operator on the weighted Dirichlet spaces Dα={f∈H（D）;‖f‖Dα^2=｜f（0）｜^2＋∫D｜f＇（z）｜^2（1-｜z｜^αdm（z）〈＋∞},where -1 〈 α 〈＋∞ and H（D） is the class of all holomorphic functions on the unit disc D.
对加权Dirichlet空间我们研究了其上一般Cesaro算子的有界性．此处H(D)表示复平面单位圆盘D上全纯函数的全体．
基金
the National Natural Science Foundation of China (10471039) the Natural Science Foundation of Zhejiang Province (103104)the Natural Science Foundation of Huzhou City (2005YZ02)the Foundation of Huzhou Teachers'College (KX21030)
参考文献11
-
1STEMPAK K, Cesaro averaging operators [J]. Proc. Roy. Soc, Edinburgh Sect. A, 1994, 124: 121-126.
-
2ANDERSEN K F. Castro averaging operators on Hardy spaces [J]. Proc, Roy. Soc. Edinburgh Sect.A, 1996,126: 617-624.
-
3XIAO Jie. Cesaro-type operators on Hardy, BMOA and Bloch spaces [J]. Arch. Math. (Basel), 1997, 68:398-406.
-
4GIANG D V, MORICZ F. The Ceshro opera,or is bounded on the Hardy space H^1 [J]. Acta Sci. Math.(Szeged), 1995, 61: 535-544.
-
5MIAO J.The Cesaro operator is bounded in H^p for 0 < p < 1 [J]. Proc. Amer. Math. Soc., 1992, 116:1077-1079.
-
6SISKAKIS A G.Composition semigroups and the Cesaro operator on H^p[J]. J. London Math. Soc., 1987,86(2): 153-164.
-
7SISKAKIS A G, The Cesaro operator is bounded on H^1[J]. Proc. Amer. Math. Soc., 1990, 110(2): 461-462.
-
8SISKAKIS A G. On the Bergman space norm of the Ceshro operator [J]. Arch. Math., 1996, 67: 312-318.
-
9GALANOPOULOS P. The Cesaro operator on Dirichlet spaces [J]. Acta Sci. Math., 2001, 67: 411-420.
-
10STEVIC S. The generalized Cesaro operator on Dirichlet spaces [J]. Studia Sci. Math. Hungar., 2003, 40(1-2):83-94.
