Opuscula Math. 37, no. 2 (2017), 303-312
Compact generalized weighted composition operators on the Bergman space
Qinghua Hu
Xiangling Zhu
Abstract.
We characterize the compactness of the generalized weighted composition operators acting on the Bergman space.
Keywords:
Bergman space, generalized weighted composition operator, compactness.
Mathematics Subject Classification:
30H30, 47B33.
References ▼
- [1] C. Cowen, B. MacCluer, Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, FL, 1995.
- [2] E. Gallardo-Gutiérrez, M. González, Hilbert-Schmidt Composition Operators on Dirichlet Spaces, AMS, 2001.
- [3] R. Hibschweiler, N. Portnoy, Composition followed by differentiation between Bergman and Hardy spaces, Rocky Mountain J. Math. 35 (2005), 843-855.
- [4] P. Karthikeyan, Compact and Hilbert-Schmidt weighted composition operators on the Bergman space, PhD Dissertation, Central Michigan University, 2008.
- [5] H. Li, X. Fu, A new characterization of generalized weighted composition operators from the Bloch space into the Zygmund space, J. Funct. Spaces Appl. 2013, Article ID 925901, 12 pp.
- [6] S. Li, S. Stević, Composition followed by differentiation between Bloch type spaces, J. Comput. Anal. Appl. 9 (2007) 2, 195-206.
- [7] S. Li, S. Stević, Composition followed by differentiation from mixed-norm spaces to \(\alpha\)-Bloch spaces, Sb. Math. 199 (2008) 12, 1847-1857.
- [8] S. Li, S. Stević, Composition followed by differentiation between \(H^{\infty}\) and \(\alpha\)-Bloch spaces, Houston J. Math. 35 (2009), 327-340.
- [9] S. Li, S. Stević Products of composition and differentiation operators from Zygmund spaces to Bloch spaces and Bers spaces, Appl. Math. Comput. 217 (2010), 3144-3154.
- [10] S. Li, S. Stević, Generalized weighted composition operators from \(\alpha\)-Bloch spaces into weighted-type spaces, J. Ineq. Appl. 2015, Article No. 265, (2015), 12 pp.
- [11] Y. Liang, Z. Zhou, Essential norm of the product of differentiation and composition operators between Bloch-type space, Arch. Math. 100 (2013), 347-360.
- [12] B. MacCluer, J. Shapiro, Angular derivatives and compact composition operators on the Hardy and Bergman spaces, Canad. J. Math. 38 (1986), 878-906.
- [13] J. Moorhouse, Compact differences of composition operators, J. Funct. Anal. 219 (2005), 70-92.
- [14] S. Stević, Norm and essential norm of composition followed by differentiation from \(\alpha\)-Bloch spaces to \(H^{\infty}_{\mu}\), Appl. Math. Comput. 207 (2009), 225-229.
- [15] S. Stević, Products of composition and differentiation operators on the weighted Bergman space, Bull. Belg. Math. Soc. Simon Stevin 16 (2009), 623-635.
- [16] S. Stević, Weighted differentiation composition operators from mixed-norm spaces to weighted-type spaces, Appl. Math. Comput. 211 (2009), 222-233.
- [17] S. Stević, Weighted differentiation composition operators from mixed-norm spaces to the weighted-type space on the unit disk, Abstr. Appl. Anal. 2010, Article ID 246287, (2010), 15 pp.
- [18] S. Stević, Weighted differentiation composition operators from \(H^{\infty}\) and Bloch spaces to \(n\)th weighted-type spaces on the unit disk, Appl. Math. Comput. 216 (2010), 3634-3641.
- [19] S. Stević, A.K. Sharma, A. Bhat, Products of multiplication composition and differentiation operators on weighted Bergman spaces, Appl. Math. Comput. 217 (2011), 8115-8125.
- [20] Y. Wu, H. Wulan, Products of differentiation and composition operators on the Bloch space, Collet. Math. 63 (2012), 93-107.
- [21] K. Zhu, Operator Theory in Function Spaces, Amer. Math. Soc., 2nd ed., 2007.
- [22] X. Zhu, Generalized weighted composition operators on weighted Bergman spaces, Numer. Funct. Anal. Opt. 30 (2009), 881-893.
- [23] X. Zhu, Generalized weighted composition operators on Bloch-type spaces, J. Ineq. Appl. (2015) 2015:59.
About the authors ▼
Qinghua Hu
Department of Mathematics, Shantou University, Guangdong Shantou 515063, P.R. China
Xiangling Zhu
Department of Mathematics, Jiaying University, Meizhou 514015, P.R. China
About the article ▼
Communicated by Stevo Stević.
Received: 2016-08-08.
Revised: 2016-08-28.
Accepted: 2016-08-28.
Published online: 2017-01-03.
Cite this article as ▼
Qinghua Hu, Xiangling Zhu, Compact generalized weighted composition operators on the Bergman space, Opuscula Math. 37, no. 2 (2017), 303-312,
http://dx.doi.org/10.7494/OpMath.2017.37.2.303.
Download this article's citation as: