Skip to main content
SpringerLink
Log in

Small Hankel Operators on the Dirichlet-Type Spaces on the Unit Ball of C n

  • ORIGINAL ARTICLES
  • Published:
Acta Mathematica Sinica Aims and scope Submit manuscript

Abstract

In this paper the small Hankel operators on the Dirichlet-type spaces D p on the unit ball of C n are considered. A similar result to that of the one-dimensional setting is given, which characterizes the boundedness of the small Hankel operators on D p .

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Karel, S.: Compact Toeplitz Operators on Bergman Spaces. Math. Proc. Camb. Phil. Soc., 124, 151–160 (1998)

    Article  Google Scholar 

  2. Hu, P. Y., Shi, J. H.: Multipliers on Dirichlet Type Spaces. Acta Mathematica Sinica, 17(2), 263–272 (2001)

    Article  Google Scholar 

  3. Hu, P. Y., Shi, J. H.: Random Dirichlet Type Functions on the Unit Ball of C n. Chin. Ann. of Math.(B), 20(3), 369–376 (1999)

    Article  Google Scholar 

  4. Hu, P. Y., Xu, W. M., Zhang, W. J.: Boundedness of Composition Operator on C p . Acta Mathematica Scientia (B), 20(3), 409–416 (2000)

    Google Scholar 

  5. Hu, P. Y., Zhang, W. J.: A New Characterization of Dirichlet Type Spaces on the Unit Ball of C n, J. of Mathematical Analysis and Applications, 259(2), 453–461 (2001)

    Article  Google Scholar 

  6. Richard, R., Wu, Z. J.: A New Characterization of Dirichlet Type Spaces and Applications. Illinois J. of Math., 37(3), 101–122 (1993)

    MathSciNet  Google Scholar 

  7. Wu, Z. J.: Hankel and Toeplitz Operators on Dirichlet Spaces. Inter. Equat. Oper. Th., 15, 503–525 (1992)

    Article  Google Scholar 

  8. Wu, Z. J.: Boundedness, Compactness and Schatten p-class of Hankel Operators Between Weighted Dirichlet Type Spaces. Ark. Mat., 31, 395–417 (1993)

    MathSciNet  Google Scholar 

  9. Karel, S., Zheng, D. C.: Teoplitz and Hankel Operators on Bergman Spaces. Trans. Amer. Math. Soc., 329(2), 773–794 (1992)

    Article  MathSciNet  Google Scholar 

  10. Karel, S.: Compact Hankel Operators on the Bergman Spaces of the Unit Ball and Polydisk in C n. J. Oper. Th., 23, 153–170 (1990)

    Google Scholar 

  11. Arazy, J., Fisher, S., Peetre, J.: Hankel Operators on Weighted Bergman Spaces. Amer. J. Math., 110, 989–1054 (1988)

    Article  MathSciNet  Google Scholar 

  12. David, A. S.: Multipliers of the Dirichlet Space. Illinois J. of Math., 24(1), 113–139 (1980)

    Google Scholar 

  13. Ron, K., Eric, S.: Carleson Measures and Multipliers of Dirichlet-Type Spaces. Trans. Amer. Math. Soc., 309(1), 87–98 (1988)

    Article  MathSciNet  Google Scholar 

  14. Carme, C., Joaquin, M. O.: Carleson Measures on Spaces of Hardy-Sobolev Type. Can. J. Math., 47(6), 1177–1200 (1995)

    Google Scholar 

  15. Carme, C., Joaquin, M. O.: On q-Carleson Measures for M-Harmonic Functions. Can. J. Math., 49(4), 653–674 (1997)

    Google Scholar 

  16. Marco, M. P.: Besov Spaces, Mean Oscillation, and Generalized Hankel Operators. Pacific J. of Math., 161(1), 155–184 (1993)

    Google Scholar 

  17. Rudin, W.: Function Theory in the Unit Ball of C n, Springer-Verlag (1980)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Normal College of Shenzhen University, Shenzhen, 518060, P. R. China

    Peng Yan Hu & Wen Jun Zhang

Authors
  1. Peng Yan Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wen Jun Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peng Yan Hu.

Additional information

This Project is Supported by National Natural Science Foundation of China, 10101013

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hu, P.Y., Zhang, W.J. Small Hankel Operators on the Dirichlet-Type Spaces on the Unit Ball of C n . Acta Math Sinica 20, 261–272 (2004). https://doi.org/10.1007/s10114-003-0253-7

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-003-0253-7

Keywords

MR (2000) Subject Classification

Search

Navigation