Skip to main content
Log in

Gleason’s problem on Fock-Sobolev spaces

  • Published:
Acta Mathematica Scientia Aims and scope Submit manuscript

Abstract

In this article, we solve completely Gleason’s problem on Fock-Sobolev spaces Fp,m for any non-negative integer m and 0 < p ≤ ∞.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bargmann V. On a Hilbert space of analytic functions and an associated integral transform. Comm Pure Appl Math, 1961, 14: 187–214

    Article  MathSciNet  Google Scholar 

  2. Janson S, Peetre J, Rochberg R. Hankel forms and the Fock space. Revista Mat Iberoamer, 1987, 3: 61–138

    Article  MathSciNet  Google Scholar 

  3. Carswell B, MacCluer B, Schuster A. Composition operators on the Fock space. Acta Sci Math (Szeged), 2003, 69: 871–887

    MathSciNet  MATH  Google Scholar 

  4. Cho H, Zhu K. Fock-Sobolev spaces and their Carleson measures. J Funct Anal, 2012, 263: 2483–2506

    Article  MathSciNet  Google Scholar 

  5. Zhu K. Analysis on Fock Spaces. New York: Springer-Verlag, 2012

    Book  Google Scholar 

  6. Hu Z. Equivalenct norms on Fock spaces with some application to extended Cesaro operators. Proc Amer Math Soc, 2013, 141: 2829–2840

    Article  MathSciNet  Google Scholar 

  7. Dai J, Wang B. A class of integral operators and the Fock space. Complex Var Elliptic Equ, 2016, 61: 562–573

    Article  MathSciNet  Google Scholar 

  8. Rudin W. Function Theory in the Unit Ball of Cn. New York: Springer-Verlag, 1980

    Book  Google Scholar 

  9. Kerzman K, Nagal A. Finitely generated ideals in certain function algebras. J Funct Anal, 1971, 7: 212–215

    Article  MathSciNet  Google Scholar 

  10. Ahern P, Schneider R. Holomorphic Lipschitz functions in pseudoconvex domains. Amer J Math, 1979, 101: 543–565

    Article  MathSciNet  Google Scholar 

  11. Zhu K. The Bergman spaces, the Bloch space and Gleason’s problem. Trans Amer Math Soc, 1988, 309: 253–268

    MathSciNet  MATH  Google Scholar 

  12. Ortega J. The gleason problem in Bergman-Sobolev spaces. Complex Var Elliptic Equ, 1992, 20: 157–170

    MathSciNet  MATH  Google Scholar 

  13. Hu Z. Gleason’s problem for harmonic mixed norm and Bloch spaces in convex domains. Math Nachr, 2006, 279: 164–178

    Article  MathSciNet  Google Scholar 

  14. Zhang X, Li M, Guan Y. The equivalent norms and the Gleason’s problem on μ-Zygmund spaces in Cn. J Math Anal Appl, 2014, 419: 185–199

    Article  MathSciNet  Google Scholar 

  15. Zhu K. Spaces of Holomorphic Functions in the Unit Ball. New York: Springer-Verlag, 2005

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Jineng Dai or Jingyun Zhou.

Additional information

Supported by the National Natural Science Foundation of China (11671306, 11771441).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dai, J., Zhou, J. Gleason’s problem on Fock-Sobolev spaces. Acta Math Sci 41, 337–348 (2021). https://doi.org/10.1007/s10473-021-0120-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10473-021-0120-6

Key words

2010 MR Subject Classification

Navigation