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The regularity of the weighted Bergman projections

Part of the Lecture Notes in Mathematics book series (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.

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References

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© 1985 Springer-Verlag

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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

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

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16050-2

  • Online ISBN: 978-3-540-39734-2

  • eBook Packages: Springer Book Archive