GENERALIZED WEIGHTED COMPOSITION OPERATORS FROM AREA NEVANLINNA SPACES TO WEIGHTED-TYPE SPACES

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 48, Issue 6, 2011, pp.1195-1205
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2011.48.6.1195

Title & Authors

GENERALIZED WEIGHTED COMPOSITION OPERATORS FROM AREA NEVANLINNA SPACES TO WEIGHTED-TYPE SPACES

Weifeng, Yang; Weiren, Yan;

Weifeng, Yang; Weiren, Yan;

Abstract

Let denote the class of all analytic functions on the open unit disk of the complex plane . Let n be a nonnegative integer, be an analytic self-map of and . The generalized weighted composition operator is defined by $$D_{{\varphi},u}^nf

Keywords

generalized weighted composition operator;area Nevanlinna space;weighted-type space;

Language

English

Cited by

1.

2.

3.

4.

5.

6.

7.

8.

References

1.

K. D. Bierstedt, J. Bonet, and J. Taskinen, Associated weights and spaces of holomorphic functions, Studia Math. 127 (1998), no. 2, 137-168.

2.

B. Choe, H. Koo, and W. Smith, Carleson measure for the area Nevalinna spaces and applications, J. Anal. Math. 104 (2008), 207-233.

3.

D. Clahane and S. Stevic, Norm equivalence and composition operators between Bloch/Lipschitz spaces of the unit ball, J. Inequal. Appl. 2006 (2006), Article ID 61018.

4.

C. Cowen and B. MacCluer, Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, 1995.

5.

X. Fu and X. Zhu, Weighted composition operators on some weighted spaces in the unit ball, Abstr. Appl. Anal. 2008 (2008), Article ID 605807.

6.

R. A. Hibschweiler and N. Portnoy, Composition followed by differentiation between Bergman and Hardy spaces, Rochy Mountain J. Math. 35 (2005), no. 3, 843-855.

7.

H. Jarchow and J. Xiao, Composition operators between Nevanlinna classes and Bergman spaces with weights, J. Operator Theory 46 (2001), no. 3, suppl., 605-618.

8.

S. Li and S. Stevic, Composition followed by differentiation between Bloch type space, J. Comput. Anal. Appl. 9 (2007), no. 2, 195-205.

9.

S. Li and S. Stevic, Weighted composition operators from $\alpha$ -Bloch space to $H^\infty$ on the polydisk, Numer. Funct. Anal. Optim. 28 (2007), no. 7-8, 911-925.

10.

S. Li and S. Stevic, Weighted composition operators from Bergman-type spaces into Bloch spaces, Proc. Indian Acad. Sci. Math. Sci. 117 (2007), no. 3, 371-385.

11.

S. Li and S. Stevic, Weighted composition operators from $H^\infty$ to the Bloch space on the polydisc, Abstr. Appl. Anal. 2007 (2007), Article ID 48478.

12.

S. Li and S. Stevic, Weighted composition operators between $H^\infty$ and $\alpha$ -Bloch spaces in the unit ball, Taiwanese J. Math. 12 (2008), no. 7, 1625-1639.

13.

S. Li and S. Stevic, Weighted composition operators from Zygmund spaces into Bloch spaces, Appl. Math. Comput. 206 (2008), no. 2, 825-831.

14.

S. Li and S. Stevic, Composition followed by differentiation from mixed-norm spaces to $\alpha$ -Bloch spaces, Matematicheskii Sbornik 199 (2008), no. 12, 117-128.

15.

Y. Liu and Y. Yu, Composition followed by differentiation between $H^\infty$ and Zygmund spaces, Complex Anal. Oper. Theory, (2010).

16.

Z. Lou, Composition operators on Bloch type spaces, Analysis (Munich) 23 (2003), no. 1, 81-95.

17.

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

18.

S. Ohno, Weighted composition operators between $H^\infty$ and the Bloch space, Taiwanese J. Math. 5 (2001), no. 3, 555-563.

19.

S. Ohno, Products of composition and differentiation between Hardy spaces, Bull. Austral. Math. Soc. 73 (2006), no. 2, 235-243.

20.

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

21.

A. L. Shields and D. L. Williams, Bounded projections, duality, and multipliers in spaces of analytic functions, J. Reine Angew. Math. 299/300 (1978), 256-279.

22.

S. Stevic, Weighted composition operators between mixed norm spaces and $H^{\infty}_\alpha$ spaces in the unit ball, J. Inequal. Appl. 2007 (2007), Article ID 28629.

23.

S. Stevic, Weighted composition operators from weighted Bergman spaces to weighted-type spaces on the unit ball, Appl. Math. Comput. 212 (2009), no. 2, 499-504.

24.

S. Stevic, Norm and essential norm of composition followed by differentiation from $\alpha$ -Bloch spaces to $H^{\infty}_\mu$ , Appl. Math. Comput. 207 (2009), no. 1, 225-229.

25.

S. Stevic, Weighted differentiation composition operators from mixed-norm spaces to weighted-type spaces, Appl. Math. Comput. 211 (2009), no. 1, 222-233.

26.

S. Stevic, Norm of weighted composition operators from $\alpha$ -Bloch spaces to weighted-type spaces, Appl. Math. Comput. 215 (2009), no. 2, 818-820.

27.

S. Stevic, Products of composition and differentiation operators on the weighted Bergman space, Bull. Belg. Math. Soc. Simon Stevin 16 (2009), no. 4, 623-635.

28.

S. Stevic, Composition followed by differentiation from $H^{\infty}$ and the Bloch space to nth weighted-type spaces on the unit disk, Appl. Math. Comput. 216 (2010), no. 12, 3450-3458.

29.

S. Stevic, Weighted differentiation composition operators from $H^{\infty}$ and Bloch spaces to nth weighted-type spaces on the unit disk, Appl. Math. Comput. 216 (2010), no. 12, 3634-3641.

30.

S. Stevic, Weighted differentiation composition operators from the mixed-norm space to the nth weigthed-type space on the unit disk, Abstr. Appl. Anal. 2010 (2010), Article ID 246287.

31.

S. Stevic, Weighted composition operators from the Bergman-Privalov-Type spaces to weighted-type spaces on the unit ball, Appl. Math. Comput. in press.

32.

J. Xiao, Compact composition operators on the area-Nevanlinna class, Exposition. Math. 17 (1999), no. 3, 255-264.

33.

J. Xiao, Composition operators: $N_\alpha$ to the Bloch space to $Q_\beta$ , Studia Math. 139 (2000), no. 3, 245-260.

34.

W. Yang, Weighted composition operators from Bloch-type spaces to weighted-type spaces, Ars Combin. 92 (2009), 415-423.

35.

W. Yang, Products of composition and differentiation operators from $Q_K$ (p, q) spaces to Bloch-type spaces, Abstr. Appl. Anal. 2009 (2009), Art. ID 741920, 14 pp.

36.

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

37.

X. Zhu, Weighted composition operators between $H^{\infty}$ and Bergman type spaces, Commun. Korean Math. Soc. 21 (2006), no. 4, 719-727.

38.

X. Zhu, Products of differentiation, composition and multiplication operator from Bergman type spaces to Bers spaces, Integral Transforms Spec. Funct. 18 (2007), no. 3-4, 223-231.

39.

X. Zhu, Generalized weighted composition operators from Bloch-type spaces to weighted Bergman spaces, Indian J. Math. 49 (2007), no. 2, 139-149.

40.

X. Zhu, Weighted composition operators from F(p, q, s) spaces to $H^{\infty}_\mu$ spaces, Abstr. Appl. Anal. 2009 (2009), Article ID 290978.

41.

X. Zhu, Generalized weighted composition operators on weighted Bergman spaces, Numer. Funct. Anal. Optim. 30 (2009), no. 7-8, 881-893.

42.

X. Zhu, Weighted composition operators from area Nevalinna spaces into Bloch spaces, Appl. Math. Comput. 215 (2010), no. 12, 4340-4346.

43.

X. Zhu, Generalized weighted composition operators on Bloch-type spaces, Ars. Combin. to appear.