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Weighted composition operators between Bers-type spaces and Bergman spaces. (English) Zbl 1125.47017
Summary: This paper characterizes the boundedness and compactness of weighted composition operators between Bers-type space (or little Bers-type space) and Bergman space. Some estimates for the norm of weighted composition operators between those spaces are obtained.

47B33 Linear composition operators
46E15 Banach spaces of continuous, differentiable or analytic functions
47A30 Norms (inequalities, more than one norm, etc.) of linear operators
Full Text: DOI
[1] Ohno Shuichi, Zhao Ruhan. Weighted composition operators on the Bloch space, Bull Austral Math Soc, 2001, 63: 177–185. · Zbl 0985.47022 · doi:10.1017/S0004972700019250
[2] Mirzakarimi G, Seddighi K. Weighted composition operators on Bergman and Dirichlet spaces, Georgian Math J, 1997, 4: 373–383. · Zbl 0891.47018 · doi:10.1023/A:1022946629849
[3] Zhao Ruhan. Composition operators from Bloch type spaces to Hardy and Besov spaces, J Math Anal Appl, 1999, 233: 749–766. · Zbl 0930.30031 · doi:10.1006/jmaa.1999.6341
[4] Hu Zhangjian, Wang Shushi. Composition operators on Bloch-type spaces, Proc Royal Soc Edinburgh, 2005, 135A: 1229–1239. · Zbl 1131.47019 · doi:10.1017/S0308210500004340
[5] Zhang Xuejun. Composition operators and weighted composition operators on p-Bloch spaces, Chinese Ann Math Ser A, 2003, 24: 711–720. · Zbl 1076.47019
[6] He Weixiang, Jiang Lijian. Composition operator on Bers-type spaces, Acta Math Sci, 2002, 22B(3): 404–412. · Zbl 1043.47023
[7] Jiang Lijian, Li Yezhou. Bers-type spaces and composition operators, Northeast Math J, 2002, 18(3): 223–232. · Zbl 1055.47021
[8] Zhao Ruhan. Pointwise multipliers from weighted Bergman spaces and Hardy spaces to weighted Bergman spaces, Annales Academiæ Scientiarum Fennicæ, 2004, 29: 139–150. · Zbl 1069.47033
[9] Metzger J A. Bounded mean oscillation and Riemann surfaces, Bounded Mean Oscillation in Complex, Joensun University, 1989: 79–100. · Zbl 0677.30029
[10] Yamashita S. Schilicht holomorphic functions and the Riccati differential equation, Math Zeit, 1997, 157: 19–22. · Zbl 0366.30005 · doi:10.1007/BF01214676
[11] Zygmund A. Trigonometric Series, UK, Cambridge: Cambridge Univ Press, 1959.
[12] Hedenmalm H, Korenblum B, Zhu K H. Theory of Bergman Spaces, GTM, 199, New York: Springer-Verlag, 2000. · Zbl 0955.32003
[13] Cowen C C, MacCluer B D. Composition Operators on Spaces of Analytic Functions, Boca Raton: CRC Press, 1995. · Zbl 0873.47017
[14] Madigan K, Matheson A. Compact composition operators on the Bloch space, Trans Amer Math Soc, 1995, 347: 2679–2687. · Zbl 0826.47023 · doi:10.2307/2154848
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