VOLTERRA COMPOSITION OPERATORS BETWEEN WEIGHTED BERGMAN SPACES AND BLOCH TYPE SPACES

Title & Authors
VOLTERRA COMPOSITION OPERATORS BETWEEN WEIGHTED BERGMAN SPACES AND BLOCH TYPE SPACES
Li, Songxiao;

Abstract
The boundedness and compactness of the Volterra composition operators between weighted Bergman spaces and Bloch type spaces are discussed in this paper.
Keywords
Volterra composition operator;Bergman space;Bloch space;
Language
English
Cited by
1.
GENERALIZED COMPOSITION OPERATORS FROM GENERALIZED WEIGHTED BERGMAN SPACES TO BLOCH TYPE SPACES,;

대한수학회지, 2009. vol.46. 6, pp.1219-1232
2.
COMPACT INTERTWINING RELATIONS FOR COMPOSITION OPERATORS BETWEEN THE WEIGHTED BERGMAN SPACES AND THE WEIGHTED BLOCH SPACES,;;

대한수학회지, 2014. vol.51. 1, pp.125-135
1.
Product of Volterra Type Integral and Composition Operators on Weighted Fock Spaces, The Journal of Geometric Analysis, 2014, 24, 2, 740
2.
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3.
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Volterra Type and Weighted Composition Operators on Weighted Fock Spaces, Integral Equations and Operator Theory, 2013, 76, 1, 81
6.
GENERALIZED COMPOSITION OPERATORS FROM GENERALIZED WEIGHTED BERGMAN SPACES TO BLOCH TYPE SPACES, Journal of the Korean Mathematical Society, 2009, 46, 6, 1219
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On an integral-type operator from logarithmic Bloch-type and mixed-norm spaces to Bloch-type spaces, Nonlinear Analysis: Theory, Methods & Applications, 2009, 71, 12, 6323
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On an integral-type operator between bloch-type spaces, Applied Mathematics and Computation, 2009, 215, 3, 954
10.
COMPACT INTERTWINING RELATIONS FOR COMPOSITION OPERATORS BETWEEN THE WEIGHTED BERGMAN SPACES AND THE WEIGHTED BLOCH SPACES, Journal of the Korean Mathematical Society, 2014, 51, 1, 125
11.
Generalized composition operators and Volterra composition operators on Bloch spaces in the unit ball, Complex Variables and Elliptic Equations, 2009, 54, 2, 95
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References
1.
A. Aleman and J. A. Cima, An integral operator on $H^p$ and Hardy's inequality, J. Anal. Math. 85 (2001), 157-176

2.
A. Aleman and A. G. Siskakis, An integral operator on $H^p$, Complex Variables Theory Appl. 28 (1995), no. 2, 149-158

3.
A. Aleman and A. G. Siskakis, Integration operators on Bergman spaces, Indiana University Math. J. 46 (1997), no. 2, 337-356

4.
J. Arazy, S. D. Fisher, and J. Peetre, Mobius invariant function spaces, J. Reine Angew. Math. 363 (1985), 110-145

5.
C. C. Cowen and B. D. MacCluer, Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, FL, 1995

6.
P. R. Halmos, Measure Theory, D. Van Nostrand Company, Inc., New York, N. Y., 1950

7.
Z. J. Hu, Extended Cesaro operators on mixed norm spaces, Proc. Amer. Math. Soc. 131 (2003), no. 7, 2171-2179

8.
Z. J. Hu, Extended Cesaro operators on the Bloch space in the unit ball of $C^n$, Acta Math. Scientia. Ser. B Engl. Ed. 23 (2003), no. 4, 561-566

9.
S. Li, Weighted composition operators from Bergman spaces into weighted Bloch spaces, Commun. Korean Math. Soc. 20 (2005), no. 1, 63-70

10.
K. Madigan and A. Matheson, Compact composition operators on the Bloch space, Trans. Amer. Math. Soc. 347 (1995), no. 7, 2679-2687

11.
S. Ohno, K. Stroethoff, and R. Zhao, Weighted composition operators between Bloch-type spaces, Rocky Mountain J. Math. 33 (2003), no. 1, 191-215

12.
F. Perez-Gonzalez and J. Rattya, Forelli-Rudin estimates, Carleson measures and F(p,q,s)-functions, J. Math. Anal. Appl. 315 (2006), no. 2, 394-414

13.
C. Pommerenke, Schlichte funktionen und analytische funktionen von beschrankter mittlerer oszillation, Comment. Math. Helv. 52 (1977), no. 4, 591-602

14.
J. H. Shapiro, Composition Operators and Classical Function Theory, Springer-Verlag, New York, 1993

15.
A. G. Siskakis and R. Zhao, A Volterra type operator on spaces of analytic functions, Function spaces(Edwardsville IL, 1998), 299-311, Contemp. Math. 232, Amer. Math. Soc. Providerce, RI, 1999

16.
S. Stevic, On an integral operator on the unit ball in $C^n$, J. Inequal. Appl. 2005 (2005), no. 1, 81-88

17.
X. M. Tang and Z. J. Hu, Composition operators between Bergman spaces and q-Bloch spaces. (Chinese) Chinese Ann. Math. Ser. A 27 (2006), no. 1, 109-118

18.
J. Xiao, Riemann-Stieltjes operators on weighted Bloch and Bergman spaces of the unit ball, J. London. Math. Soc. (2) 70 (2004), no. 1, 199-214

19.
R. Yoneda, Pointwise multipliers from BMOA$^{\alpha}$ to BMOA$^{beta}$, Complex Var. Theory Appl. 49 (2004), no. 14, 1045-1061

20.
R. H. Zhao, Composition operators from Bloch type spaces to Hardy and Besov spaces, J. Math. Anal. Appl. 233 (1999), no. 2, 749-766

21.
K. Zhu, Operator Theory in Function Spaces, Monographs and Textbooks in Pure and Applied Mathematics, 139. Marcel Dekker, Inc., New York, 1990

22.
K. Zhu, Spaces of Holomorphic Functions in the Unit Ball, Graduate Texts in Mathematics, 226. Springer-Verlag, New York, 2005