We study when a weighted composition operator acting between different weighted Bergman spaces is bounded, resp. compact.
@article{bwmeta1.element.doi-10_2478_v10062-012-0008-y,
author = {Elke Wolf},
title = {Boundedness and compactness of weighted composition operators between weighted Bergman spaces},
journal = {Annales UMCS, Mathematica},
volume = {66},
year = {2012},
pages = {75-75},
zbl = {1277.47037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10062-012-0008-y}
}
Elke Wolf. Boundedness and compactness of weighted composition operators between weighted Bergman spaces. Annales UMCS, Mathematica, Tome 66 (2012) p. 75. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10062-012-0008-y/
Bonet, J., Domański, P. and Lindström, M., Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions, Canad. Math. Bull. 42 (1999), no. 2, 139-148. | Zbl 0939.47020
Bonet, J., Domański, P., Lindström, M. and Taskinen, J., Composition operators between weighted Banach spaces of analytic functions, J. Austral. Math. Soc. Ser. A 64 (1998), no. 1, 101-118. | Zbl 0912.47014
Bonet, J., Friz, M. and Jordá, E., Composition operators between weighted inductive limits of spaces of holomorphic functions, Publ. Math. Debrecen 67 (2005), no. 3-4, 333-348. | Zbl 1097.46013
Contreras, M. D., Hernández-Díaz, A. G., Weighted composition operators in weighted Banach spaces of analytic functions, J. Austral. Math. Soc. Ser. A 69 (2000), no. 1, 41-60. | Zbl 0990.47018
Cowen, C., MacCluer, B., Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1995. | Zbl 0873.47017
Cučković, Z., Zhao, R., Weighted composition operators on the Bergman space, J. London Math. Soc. (2) 70 (2004), no. 2, 499-511. | Zbl 1069.47023
Duren, P., Schuster, A., Bergman Spaces, Mathematical Surveys and Monographs, 100, American Mathematical Society, Providence, RI, 2004.
Hastings, W., A Carleson measure theorem for Bergman spaces, Proc. Amer. Math. Soc. 52 (1975), 237-241. | Zbl 0296.31009
Hedenmalm, H., Korenblum, B. and Zhu, K., Theory of Bergman spaces, Graduate Texts in Mathematics, 199, Springer-Verlag, New York, 2000. | Zbl 0955.32003
Kriete, T., MacCluer, B., Composition operators on large weighted Bergman spaces, Indiana Univ. Math. J. 41 (1992), no. 3, 755-788. | Zbl 0772.30043
Moorhouse, J., Compact differences of composition operators, J. Funct. Anal. 219 (2005), no. 1, 70-92. | Zbl 1087.47032
MacCluer, B., Ohno, S. and Zhao, R., Topological structure of the space of composition operators on H∞, Integral Equations Operator Theory 40 (2001), no. 4, 481-494. | Zbl 1062.47511
Nieminen, P., Compact differences of composition operators on Bloch and Lipschitz spaces, Comput. Methods Funct. Theory 7 (2007), no. 2, 325-344. | Zbl 1146.47016
Palmberg, N., Weighted composition operators with closed range, Bull. Austral. Math. Soc. 75 (2007), no. 3, 331-354. | Zbl 1123.47028
Shapiro, J. H., Composition Operators and Classical Function Theory, Universitext: Tracts in Mathematics. Springer-Verlag, New York, 1993.
Wolf, E., Weighted composition operators between weighted Bergman spaces, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM 103 (2009), no. 1, 11-15. | Zbl 1197.47041