We study when a weighted composition operator acting between different weighted Bergman spaces is bounded, resp. compact.
@article{bwmeta1.element.ojs-doi-10_17951_a_2012_66_1_75-81,
author = {Elke Wolf},
title = {Boundedness and compactness of weighted composition operators between weighted Bergman spaces},
journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica},
volume = {66},
year = {2012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2012_66_1_75-81}
}
Elke Wolf. Boundedness and compactness of weighted composition operators between weighted Bergman spaces. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 66 (2012) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2012_66_1_75-81/
Bonet, J., Domański, P. and Lindstrom, 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.
Bonet, J., Domański, P., Lindstrom, 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.
Bonet, J., Friz, M. and Jorda, E., Composition operators between weighted inductive limits of spaces of holomorphic functions, Publ. Math. Debrecen 67 (2005), no. 3-4, 333-348.
Contreras, M. D., Hernandez-Dıaz, A. G., Weighted composition operators in weighted Banach spaces of analytic functions, J. Austral. Math. Soc. Ser. A 69 (2000), no. 1, 41-60.
Cowen, C., MacCluer, B., Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1995.
Cuckovic, Z., Zhao, R., Weighted composition operators on the Bergman space, J. London Math. Soc. (2) 70 (2004), no. 2, 499-511.
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.
Hedenmalm, H., Korenblum, B. and Zhu, K., Theory of Bergman spaces, Graduate Texts in Mathematics, 199, Springer–Verlag, New York, 2000.
Kriete, T., MacCluer, B., Composition operators on large weighted Bergman spaces, Indiana Univ. Math. J. 41 (1992), no. 3, 755-788.
Moorhouse, J., Compact differences of composition operators, J. Funct. Anal. 219 (2005), no. 1, 70-92.
MacCluer, B., Ohno, S. and Zhao, R., Topological structure of the space of composition operators on , Integral Equations Operator Theory 40 (2001), no. 4, 481-494.
Nieminen, P., Compact differences of composition operators on Bloch and Lipschitz spaces, Comput. Methods Funct. Theory 7 (2007), no. 2, 325-344.
Palmberg, N., Weighted composition operators with closed range, Bull. Austral. Math. Soc. 75 (2007), no. 3, 331-354.
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 F´ıs. Nat. Ser. A Math. RACSAM 103 (2009), no. 1, 11-15.