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Weighted composition operators on weighted Bergman and Dirichlet spaces

Part of: Special classes of linear operators

Published online by Cambridge University Press:  28 April 2022

Kobra Esmaeili Open the ORCID record for Kobra Esmaeili [Opens in a new window]  and
Karim Kellay
Kobra Esmaeili*
Affiliation:
Faculty of Engineering, Ardakan University, Ardakan, Yazd 89518-95491, Iran
Karim Kellay
Affiliation:
CNRS, Bordeaux INP, IMB, UMR 5251, University of Bordeaux, Talence 33405, France e-mail: kkellay@math.u-bordeaux.fr
*
e-mail: esmaeili@ardakan.ac.ir
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Abstract

We study the boundedness and compactness of weighted composition operators acting on weighted Bergman spaces and weighted Dirichlet spaces by using the corresponding Carleson measures. We give an estimate for the norm and the essential norm of weighted composition operators between weighted Bergman spaces as well as the composition operators between weighted Hilbert spaces.

Keywords

Weighted composition operatorsboundednesscompactnessCarleson measuresBergman spacesDirichlet spacesweighted Hilbert spaces

MSC classification

Primary: 47B33: Composition operators
Secondary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 66 , Issue 1 , March 2023 , pp. 286 - 302
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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Footnotes

The research of the first author is supported by a grant by the Embassy of France in Iran. The research of the second author is partially supported by the project ANR-18-CE40-0035.

References

Bao, G. and Wulan, H., Hankel matrices acting on Dirichlet spaces . J. Math. Anal. Appl. 409(2014), no. 1, 228–235.CrossRefGoogle Scholar
Constantin, O., Carleson embeddings and some classes of operators on weighted Bergman spaces . J. Math. Anal. Appl. 365(2010), no. 1, 668–682.CrossRefGoogle Scholar
Contreras, M. D., Peláez, J. A., Pommerenke, C., and Rättyä, J., Integral operators mapping into the space of bounded analytic functions . J. Funct. Anal. 271(2016), no. 10, 2899–2943.CrossRefGoogle Scholar
Cowen, C. and MacCluer, B., Composition operators on spaces of analytic functions, CRC Press, Boca Raton, 1995.Google Scholar
Čučković, Z. and Zhao, R., Weighted composition operators on the Bergman space . J. Lond. Math. Soc. 70(2004), no. 2, 499–511.Google Scholar
Čučković, Z. and Zhao, R., Weighted composition operators between weighted Bergman spaces and different hardy spaces . Ill. J. Math. 51(2007), no. 2, 479–498.Google Scholar
Duren, P. and Schuster, A., Bergman spaces, Mathematical Surveys and Monographs, 100, American Mathematical Society, Providence, RI, 2004.Google Scholar
El-Fallah, O., Mahzouli, H., Marrhich, I., and Naqos, H., Toeplitz operators on harmonically weighted Bergman spaces and applications to composition operators on Dirichlet spaces . J. Math. Anal. Appl. 466(2018), no. 1, 471–489.CrossRefGoogle Scholar
Hastings, W. W., A Carleson measure theorem for Bergman spaces . Proc. Amer. Math. Soc. 52(1975), 237–241.CrossRefGoogle Scholar
Kellay, K. and Lefèvre, P., Compact composition operators on weighted Hilbert spaces of analytic functions . J. Math. Anal. Appl. 386(2012), 718–727.CrossRefGoogle Scholar
Kriete, T. L. III and MacCluer, B., Composition operators on large weighted Bergman spaces . Indiana Univ. Math. J. 41(1992), no. 3, 755–788.CrossRefGoogle Scholar
Lindström, M. and Saukko, E., Norm of weighted composition operators and difference of composition operators between standard weighted Bergman spaces . Complex Anal. Oper. Theory 9(2015), no. 6, 1411–1432.CrossRefGoogle Scholar
Luecking, D. H., Forward and reverse Carleson inequalities for functions in Bergman spaces and their derivatives . Amer. J. Math. 107(1985), 85–111.Google Scholar
Pau, J. and Pérez, P. A., Composition operators acting on weighted Dirichlet spaces . J. Math. Anal. Appl. 401(2013), no. 2, 682–694.CrossRefGoogle Scholar
Stevic, S. and Sharma, A., Generalized composition operators on weighted hardy spaces . Appl. Math. Comput. 218(2012), 8347–8352.Google Scholar
Zhu, K., Positive Toeplitz operators on weighted Bergman spaces of bounded symmetric domains . J. Operator Theory 20(1988), no. 2, 329–357.Google Scholar
Zhu, K., Operator theory in function spaces. 2nd ed., Mathematical Surveys and Monographs, 138, American Mathematical Society, Providence, RI, 2007.CrossRefGoogle Scholar