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SCHATTEN-HERZ CLASS TOEPLITZ OPERATORS ON WEIGHTED BERGMAN SPACES INDUCED BY DOUBLING WEIGHTS

  • Du, Juntao (Department of Mathematics Shantou University) ;
  • Li, Songxiao (Institute of Fundamental and Frontier Sciences University of Electronic Science and Technology of China)
  • Received : 2020.06.26
  • Accepted : 2020.11.02
  • Published : 2021.05.31
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Abstract

Schatten-Herz class Toeplitz operators on weighted Bergman spaces induced by doubling weights are investigated in this paper.

Keywords

Acknowledgement

The project was supported by NNSF of China (No.11720101003).

References

  1. B. Choe, H. Koo, and K. Na, Positive Toeplitz operators of Schatten-Herz type, Nagoya Math. J. 185 (2007), 31-62. https://doi.org/10.1017/S0027763000025733
  2. E. S. Choi and K. Na, Schatten-Herz type positive Toeplitz operators on pluriharmonic Bergman spaces, J. Math. Anal. Appl. 327 (2007), no. 1, 679-694. https://doi.org/10.1016/j.jmaa.2006.04.032
  3. Z. Hu and X. Tang, Schatten(-Herz) class extended Cesaro operators on Bergman spaces in the unit ball of Cn, Proc. Amer. Math. Soc. 138 (2010), no. 8, 2803-2814. https://doi.org/10.1090/S0002-9939-10-10365-7
  4. M. Loaiza, M. Lopez-Garcia, and S. Perez-Esteva, Herz classes and Toeplitz operators in the disk, Integral Equations Operator Theory 53 (2005), no. 2, 287-296. https://doi.org/10.1007/s00020-004-1320-x
  5. X. F. Lu and Z. J. Hu, Schatten(-Herz) classes of Toeplitz operators on weighted Bergman spaces, Acta Math. Sinica (Chin. Ser.) 53 (2010), no. 4, 699-716.
  6. X. F. Lu and Z. J. Hu, Schatten-Herz class Toeplitz operators on harmonic Bergman spaces of smooth domains in Rn, Math. Nachr. 286 (2013), no. 2-3, 248-259. https://doi.org/10.1002/mana.201100062
  7. J. Pelaez, Small weighted Bergman spaces, in Proceedings of the Summer School in Complex and Harmonic Analysis, and Related Topics, 29-98, Publ. Univ. East. Finl. Rep. Stud. For. Nat. Sci., 22, Univ. East. Finl., Fac. Sci. For., Joensuu, 2016.
  8. J. Pelaez and J. Rattya, Weighted Bergman spaces induced by rapidly increasing weights, Mem. Amer. Math. Soc. 227 (2014), no. 1066, vi+124 pp.
  9. J. Pelaez and J. Rattya, Trace class criteria for Toeplitz and composition operators on small Bergman spaces, Adv. Math. 293 (2016), 606-643. https://doi.org/10.1016/j.aim.2016.02.017
  10. J. Pelaez and J. Rattya, Two weight inequality for Bergman projection, J. Math. Pures Appl. (9) 105 (2016), no. 1, 102-130. https://doi.org/10.1016/j.matpur.2015.10.001
  11. J. Pelaez, J. Rattya, and K. Sierra, Berezin transform and Toeplitz operators on Bergman spaces induced by regular weights, J. Geom. Anal. 28 (2018), no. 1, 656-687. https://doi.org/10.1007/s12220-017-9837-9
  12. K. Zhu, Operator theory in function spaces, second edition, Mathematical Surveys and Monographs, 138, American Mathematical Society, Providence, RI, 2007. https://doi.org/10.1090/surv/138