Composition Operators Between the Weighted Dirichlet Spaces on Bounded Symmetric Domains of C^n
被引量:2
Composition Operators Between the Weighted Dirichlet Spaces on Bounded Symmetric Domains of C^n
摘要
In this paper, we define the weighted Dirichlet space D p α(Ω) on bounded symmetric domains Ω of C n. Using η-α Carleson measure,we study the boundedness and compactmess of the composition operators between the weighted Dirichlet spaces.
参考文献6
-
1Zhu K H,Harmonic Analysis in China,1995年,287页
-
2Shi J H,Trans Amer Nucl Soc,1991年,328卷,619页
-
3D Bekolle,J Funct Anal,1990年,93卷,310页
-
4Zhu K H,Operator theory in function space,1990年
-
5C A Berger,Am J Math,1988年,110卷,921页
-
6Luo L,Chin Ann Math B
同被引文献18
-
1[4]Smith W. Composition operators between Bergman and Hardy spaces[J]. Trans. Amer. Math. Soc., 1996, 348(6):2331-2348.
-
2[5]Zhu Kehe. Operator Theory in Ftnction Space[M]. New York: Marcel Dekker, 1990.
-
3[6]Li Huiping. Hankel operators on Bergman spaces of strongly psetdoconvex domains[J]. Intergral Equation operator theory, 1994, (19) :458 -476.
-
4[7]Li Huiping, BMO. VMO and Hankel operators on the Bergman space of strongly pseudooonves domains[J]. Journal Functional Analysis, 1992,(106):375-408.
-
5[8]Pavlovic M. Inequalities for the gradient of eighenfunctions of the invariant laplacian on the unit ball[J]. Indag. Math., 1991, (2):89-98.
-
6[9]Bekolle D, Berger C.A, coburn L.A, etc. BMO in the Bergman metric on bounded symmetric domains[J]. J. Funct. Anal. 1990, (93):310-350.
-
7[10]Halrmos, P.R.. Measure theory[M]. 1951.
-
8[11]Krants S.G. Function theory of several complex variables[M]. New York: John Wiley and Sons, 1982.
-
9SMFTH W. Composition Operators Between Bergman and Hardy Spaces Trans[J]. Amer. Math. Soc. ,1996,348(6):2331 ~2348.
-
10SHAPIRO J H. Composition Operators and Classical Function Theory[M]. New York: Springer- verlag, 1993.9 ~ 20.