Abstract
In this paper, we characterize bounded, compact or Schatten class weighted composition operators acting on Bergman spaces with the exponential type weights. Moreover, we give the proof of the necessary part for the boundedness of \(C_\phi \) on large weighted Bergman spaces given by Kriete and MacCluer (J Indiana Univ Math 1(3):755–788, 1992).
Similar content being viewed by others
References
Asserda, S., Hichame, A.: Pointwise estimate for the Bergman kernel of the weighted Bergman spaces with exponential type weights. C. R. Acad. Sci. Paris Ser. I 352, 13–16 (2014)
Arroussi, H., Park, I., Pau, J.: Schatten class Toeplitz operators acting on large weighted Bergman spaces. Studia Math. 352, 203–221 (2015)
Chalendar, I., Gallardo-Gutiérrez, E.A., Partington, J.R.: Weighted composition operators on the Dirichlet space: boundedness and spectral properties. Math. Annalen. 363, 1265–1279 (2015)
Contreras, M.D., Hernandez-Diaz, A.G.: Weighted composition operators on Hardy spaces. J. Math. Anal. Appl 263, 224–233 (2001)
Cowen, C., MacCluer, B.: Composition Operators on Spaces of Analytic Functions. CRC Press, Boca Raton (1995)
Cuckovic, Z., Zhao, R.: Weighted composition operators on the Bergman space. J. Lond. Math. Soc. 70, 499–511 (2004)
Halmos, P.: Measure Theory. Springer, Berlin (1974)
Kriete, T., MacCluer, B.: Composition operators on large weighted Bergman spaces. J. Indiana Univ. Math. 41(3), 755–788 (1992)
Lin, P., Rochberg, R.: Hankel operators on the weighted Bergman spaces with exponential type weights. Integr. Equ. Oper. Theory 21, 460–483 (1995)
Ohno, S., Zhao, R.: Weighted composition operators on the Bloch space. Bull. Austral. Math. Soc. 63, 177–185 (2001)
Oleinik, V.L.: Embedding theorems for weighted classes of harmonic and analytic functions. J. Soviet Math. 9, 228–243 (1978)
Pau, J., Peláez, J.A.: Embedding theorems and integration operators on Bergman spaces with rapidly decreasing weights. J. Funct. Anal. 259, 2727–2756 (2010)
Peláez, J.A., Rättyä, J.: Trace class criteria for Toeplitz and composition operators on small Bergman spaces. Adv. Math. 293, 606–643 (2016)
Shapiro, J.H.: The essential norm of a composition operator. Ann. Math. 125, 375–404 (1987)
Sharma, A.K., Ueki, S.I.: Composition operators between weighted Bergman spaces with admissible Bekollé weights. Banach J. Math. Anal. 8, 64–88 (2014)
Zhu, K.: Operator Theory in Function Spaces. Marcel Dekker, New York (1990)
Acknowledgements
The author would like to thank the referee for indicating various mistakes and giving helpful comments.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Scott McCullough.
Rights and permissions
About this article
Cite this article
Park, I. The Weighted Composition Operators on the Large Weighted Bergman Spaces. Complex Anal. Oper. Theory 13, 223–239 (2019). https://doi.org/10.1007/s11785-018-0768-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11785-018-0768-7