Schatten class weighted composition operators on Bergman spaces of bounded strongly pseudoconvex domains

Xiangdong Yang

Open Mathematics (2013)

  • Volume: 11, Issue: 1, page 74-84
  • ISSN: 2391-5455

Abstract

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We characterize the Schatten class weighted composition operators on Bergman spaces of bounded strongly pseudoconvex domains in terms of the Berezin transform.

How to cite

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Xiangdong Yang. "Schatten class weighted composition operators on Bergman spaces of bounded strongly pseudoconvex domains." Open Mathematics 11.1 (2013): 74-84. <http://eudml.org/doc/269608>.

@article{XiangdongYang2013,
abstract = {We characterize the Schatten class weighted composition operators on Bergman spaces of bounded strongly pseudoconvex domains in terms of the Berezin transform.},
author = {Xiangdong Yang},
journal = {Open Mathematics},
keywords = {Weighted composition operators; Bergman spaces; Schatten class; weighted composition operators},
language = {eng},
number = {1},
pages = {74-84},
title = {Schatten class weighted composition operators on Bergman spaces of bounded strongly pseudoconvex domains},
url = {http://eudml.org/doc/269608},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Xiangdong Yang
TI - Schatten class weighted composition operators on Bergman spaces of bounded strongly pseudoconvex domains
JO - Open Mathematics
PY - 2013
VL - 11
IS - 1
SP - 74
EP - 84
AB - We characterize the Schatten class weighted composition operators on Bergman spaces of bounded strongly pseudoconvex domains in terms of the Berezin transform.
LA - eng
KW - Weighted composition operators; Bergman spaces; Schatten class; weighted composition operators
UR - http://eudml.org/doc/269608
ER -

References

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  1. [1] Abate M., Saracco A., Carleson measures and uniformly discrete sequences in strongly pseudoconvex domains, J. London Math. Soc. (in press), DOI: 10.1112/jlms/jdq092 Zbl1227.32008
  2. [2] Arazy J., Fisher S.D., Peetre J., Hankel operators on weighted Bergman spaces, Amer. J. Math., 1988, 110(6), 989–1053 http://dx.doi.org/10.2307/2374685 Zbl0669.47017
  3. [3] Čučkovic Ž., Zhao R., Weighted composition operators on the Bergman space, J. London Math. Soc., 2004, 70(2), 499–511 http://dx.doi.org/10.1112/S0024610704005605 Zbl1069.47023
  4. [4] Čučkovic Ž., Zhao R., Essential norm estimate of weighted composition operators between Bergman spaces on strongly pseudoconvex domains, Math. Proc. Cambridge Philos. Soc., 2007, 142(3), 525–533 http://dx.doi.org/10.1017/S0305004106009893 Zbl1126.47024
  5. [5] Kobayashi S., Hyperbolic Complex Spaces, Grundlehren Math. Wiss., 318, Springer, Berlin, 1998 Zbl0917.32019
  6. [6] Li S.-Y., Trace ideal criteria for composition operators on Bergman spaces, Amer. J. Math., 1995, 117(5), 1299–1323 http://dx.doi.org/10.2307/2374977 Zbl0983.47018
  7. [7] Zhu K.H., Positive Toeplitz operators on weighted Bergman spaces of bounded symmetric domains, J. Operator Theory, 1988, 20(2), 329–357 Zbl0676.47016
  8. [8] Zhu K.H., Operator Theory in Function Spaces, Monogr. Textbooks Pure Appl. Math., 139, Marecl Dekker, New York, 1990 Zbl0706.47019

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