Skip to main content
Log in

Bounded and Invertible Toeplitz Products on Vector Weighted Bergman Spaces of the Unit Polydisc

  • Published:
Mediterranean Journal of Mathematics Aims and scope Submit manuscript

Abstract

We characterize bounded and invertible Toeplitz products on vector weighted Bergman spaces of the unit polydisc. For our purpose, we will need the notion of Békollé–Bonami weights in several parameters.

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. Aleman, A., Pott, S., Reguera, M.C.: Sarason conjecture on Bergman space. arXiv:1304.1750. To appear in Intern. Math. Res. Notices

  2. Békollé, D.:Inégalités à poids pour le project de Bergman dans la boule unité de \({\mathbb{C}}^n\). Weighted inequalities for the Bergman projection in the unit ball of Cn. Stud. Math. 71(3), 305–323 (1981/82) (French)

  3. Békollé, D., Bonami, A.: Inégalités à poids pour le noyau de Bergman. Weighted inequalities for the Bergman kernel. C. R. Acad. Sci. Paris Sér. A–B 286(18), A775–A778 (1978) (French)

  4. Isralowitz, J.: Invertible Toeplitz products, weighted inequalities and \(A_p\) weights. J. Oper. Theor. 71(2), 381–410 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  5. Lu, Y., Sun, Z.: Invertible Toeplitz operators products on the Bergman spaces of the polydisc. J. Math. Res. Appl. Sept. 32(5), 543–553 (2012)

    MathSciNet  MATH  Google Scholar 

  6. Miao, J.: Bounded Toeplitz products on the weighted Bergman spaces of the unit ball. J. Math. Anal. Appl. 346, 305–313 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Pott, S., Reguera, M.C.: Sharp Békollé estimates for the Bergman projection. J. Funct. Anal. 265, 3233–3244 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Stroethoff, K., Zheng, A.D.: Invertible Toeplitz products. J. Funct. Anal. 195(1), 48–70 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  9. Stroethoff, K., Zheng, A.D.: Bounded Toeplitz products on the Bergman space of the polydisk. J. Math. Anal. Appl. 278(1), 125–135 (2003)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Benoit F. Sehba.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sehba, B.F. Bounded and Invertible Toeplitz Products on Vector Weighted Bergman Spaces of the Unit Polydisc. Mediterr. J. Math. 14, 178 (2017). https://doi.org/10.1007/s00009-017-0978-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00009-017-0978-7

Mathematics Subject Classification

Keywords

Navigation