Compact generalized weighted composition operators on the Bergman space

• Autorzy: Hu O. , Zhu X.

Identyfikatory

DOI

10.7494/OpMath.2017.37.2.303

• Języki publikacji: EN

Abstrakty

EN

We characterize the compactness of the generalized weighted composition operators acting on the Bergman space.

Słowa kluczowe

EN

Bergman space; generalized weighted composition operator; compactness

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2017
• Tom: Vol. 37, no. 2
• Strony: 303--312
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Hu O.

• Department of Mathematics Shantou University Guangdong Shantou 515063, P.R. China

autor

Zhu X.

• Department of Mathematics Jiaying University Meizhou 514015, P.R. China

Bibliografia

• [1] C. Cowen, B. MacCluer, Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, FL, 1995.
• [2] E. Gallardo-Gutierrez, M. Gonzalez, 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, [6] 12 pp.
• [6] S. Li, S. Stevie, Composition followed by differentiation between Bloch type spaces, J. Comput. Anal. Appl. 9 (2007) 2, 195-206.
• [7] S. Li, S. Stevie, Composition followed by differentiation from, mixed-norm, spaces to a-Bloch spaces, Sb. Math. 199 (2008) 12, 1847-1857.
• [8] S. Li, S. Stevie, Composition followed by differentiation between 77°° and a-Bloch spaces, Houston J. Math. 35 (2009), 327-340.
• [9] S. Li, S. Stevie, 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. Stevie, Generalized weighted composition operators from a-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. Stevie, Norm and essential norm, of composition followed by differentiation from, a-Bloch spaces to Hff, Appl. Math. Comput. 207 (2009), 225-229.
• [15] S. Stevie, Products of composition and differentiation operators on the weighted Bergman space, Bull. Belg. Math. Soc. Simon Stevin 16 (2009), 623-635.
• [16] S. Stevie, Weighted differentiation composition operators from mixed-norm, spaces to weighted-type spaces, Appl. Math. Comput. 211 (2009), 222-233.
• [17] S. Stevie, Weighted differentiation composition operators from mixed-norm spaces to the nth weighted-type space on the unit disk, Abstr. Appl. Anal. 2010, Article ID 246287, (2010), 15 pp.
• [18] S. Stevie, Weighted differentiation composition operators from 77°° and Bloch spaces to nth weighted-type spaces on the unit disk, Appl. Math. Comput. 216 (2010), 3634-3641.
• [19] S. Stevie, 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. OPUSCULA MATHEMATICA [25] (2015) 2015:59.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).