Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-26T07:39:36.687Z Has data issue: false hasContentIssue false
  • English
  • Français

Essential norm estimates of weighted composition operators between Bergman spaces on strongly pseudoconvex domains

Published online by Cambridge University Press:  01 May 2007

ŽELJKO ČUČKOVIĆ  and
RUHAN ZHAO
ŽELJKO ČUČKOVIĆ
Affiliation:
Department of Mathematics, University of Toledo, Toledo, OH 43606-3390, U.S.A. e-mail: [email protected]
RUHAN ZHAO
Affiliation:
Department of Mathematics, SUNY-Brockport, Brockport, NY 14420, U.S.A. e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We give estimates of the essential norms of weighted composition operators acting between Bergman spaces on strongly pseudoconvex domains. We also characterize boundedness and compactness of these operators.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 142 , Issue 3 , May 2007 , pp. 525 - 533
Copyright
Copyright © Cambridge Philosophical Society 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Beatrous, F. and Li, S-Y.. On the boundedness and compactness of operators of Hankel type. J. Funct. Anal. 111 (1993), 350–379.CrossRefGoogle Scholar
[2]Brown, L. and Shields, A. L.. Cyclic vectors in the Dirichlet space. Trans. Amer. Math. Soc. 285 (1994), 269–304.CrossRefGoogle Scholar
[3]Contreras, M. D. and Hernández–Díaz, A. G.. Weighted composition operators on Hardy spaces. J. Math. Anal. Appl. 263 (2001), 224–233.CrossRefGoogle Scholar
[4]Contreras, M. D. and Hernández–Díaz, A. G.. Weighted composition operators between different Hardy spaces. Integral Equations Operator Theory 146 (2003), 165–188.CrossRefGoogle Scholar
[5]ČuČković, Ž. and Zhao, R.. Weighted composition operators on the Bergman space. J. London Math. Soc. 170 (2004), 499–511.Google Scholar
[6]ČuČković, Ž. and Zhao, R. Weighted composition operators between different weighted Bergman spaces and differerent Hardy spaces. Illinois J. Math., to appear.Google Scholar
[7]Fefferman, C.. The Bergman kernel and biholomorphic mappings of pseudoconvex domains. Invent. Math. 26 (1974), 1–65.CrossRefGoogle Scholar
[8]Gorkin, P. and MacCluer, B.. Essential norms of composition operators. Integral Equations Operator Theory 48 (2004), 27–40.CrossRefGoogle Scholar
[9]Jarchow, H.. Compactness properties of composition operators. Rend. Circ. Mat. Palermo 2 (1998), 91–97.Google Scholar
[10]Kerzman, N.. The Bergman kernel function. Differentiability at the boundary. Math. Ann. 195 (1972), 149–158.CrossRefGoogle Scholar
[11]Krantz, S. G.. Function Theory of Several Complex Variables (AMS Chelsea Publishing, 2001).CrossRefGoogle Scholar
[12]Krantz, S. G. and Li, S–Y.. A note on Hardy spaces and functions of bounded mean oscillation on domains in . Michigan Math. J. 41 (1994), 51–71.CrossRefGoogle Scholar
[13]Li, S–Y.. Trace ideal criteria for composition operators on Bergman spaces. Amer. J. Math. 117 (1995), 1299–1323.CrossRefGoogle Scholar
[14]Luecking, D. H.. Forward and reverse Carleson inequalities for functions in Bergman spaces and their derivatives. Amer. J. Math. 107 (1985), 85–111.CrossRefGoogle Scholar
[15]Ohno, S., Stroethoff, K. and Zhao, R.. Weighted composition operators between Bloch-type spaces. Rocky Mountain J. Math. 33 (2003), 191–215.CrossRefGoogle Scholar
[16]Poggi–Corradini, P.. The essential norm of composition operators revisited. Contemporary Math. 213 (1998), 167–173.CrossRefGoogle Scholar
[17]Phong, D. H. and Stein, E. M.. Estimates for the Bergman and Szegö projections on strongly pseudo-convex domains. Duke Math. J. 44 (1977), 695–704.CrossRefGoogle Scholar
[18]Riedl, R.. Composition operators and geometric properties of analytic functions (Thesis, Universität Zurich, 1994).Google Scholar
[19]Shapiro, J. H.. The essential norm of a composition operator. Ann. Math. 125 (1987), 375–404.CrossRefGoogle Scholar
[20]Smith, W.. Composition operators between Bergman and Hardy spaces. Trans. Amer. Math. Soc. 348 (1996), 2331–2348.CrossRefGoogle Scholar
[21]Smith, W. and Yang, L.Composition operators that improve integrability on weighted Bergman spaces. Proc. Amer. Math. Soc. 126 (1998), 411–420.CrossRefGoogle Scholar