Skip to main content
SpringerLink
Log in

The regularity of the weighted Bergman projections

  • Conference paper
  • First Online:
Seminar on Deformations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1165))

Abstract

In the paper the following fact is proved: If D is a smooth pseudoconvex bounded domain such that for some s > 0 there exists a compact operator Ts : W s<0;1> (D)→Ws(D) solving the \(\bar \partial\)-problem \((\bar \partial T_s W = W)\), then for each \(w \in C^\infty (\bar D)\), the weighted Bergman projection with weight eW is a continuous operator from Ws(D) into Ws(D).

We also study some other weighted Bergman projections related to the defining function σ of the domain D.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. AHERN, P. and R. SCHNEIDER, Holomorphic Lipschitz functions in pseudoconvex domains, Amer. J. Math. 101 (1979), 543–565.

    Article  MathSciNet  MATH  Google Scholar 

  2. BELL, S., Proper holomorphic mappings and the Bergman projection, Duke Math. J. 48 (1981), 167–175.

    Article  MathSciNet  MATH  Google Scholar 

  3. —, Biholomorphic mappings and the \(\bar \partial\)-problem, Ann. of Math. 114 (1981), 103–113.

    Article  MathSciNet  MATH  Google Scholar 

  4. — and E. LIGOCKA, A simplification and extension of Fefferman's theorem on biholomorphic mappings, Invent. Math. 57 (1980), 283–289.

    Article  MathSciNet  MATH  Google Scholar 

  5. HENKIN, G. and. ROMANOV, Exact Hölder estimates for solutions of \(\bar \partial\)-problem (in Russian), Izv. Akad. IV Ser. Mat. 35 (1971), 1171–1183.

    MathSciNet  Google Scholar 

  6. KOHN, J.J., Global regularity for \(\bar \partial\)on weakly pseudoconvex manifolds, Trans. Amer. Math. Soc. 181 (1973), 273–291.

    MathSciNet  MATH  Google Scholar 

  7. LIGOCKA, E., The Hölder continuity of the Bergman projection and proper holomorphic mappings, Studia Math., to appear.

    Google Scholar 

  8. BELL, S. and H. BOAS, Regularity of the Bergman projections in weakly pseudoconvex domains, Ann. of Math. 257 (1981), 23–30.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics of the Polish Academy of Sciences Śniadeckich 8, P.O.Box 137, PL-00-950, Warszawa, Poland

    Ewa Ligocka

Authors
  1. Ewa Ligocka
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Julian Ławrynowicz

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Ligocka, E. (1985). The regularity of the weighted Bergman projections. In: Ławrynowicz, J. (eds) Seminar on Deformations. Lecture Notes in Mathematics, vol 1165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076154

Download citation

  • DOI: https://doi.org/10.1007/BFb0076154

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16050-2

  • Online ISBN: 978-3-540-39734-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation