A survey of the \(L^p\) regularity of the Bergman projection

Abstract

Although the Bergman projection operator \({\mathbf{B}}_{\Omega }\) is defined on \(L^2(\Omega )\), its behavior on other \(L^p(\Omega )\) spaces for \(p\not =2\) is an active research area. We survey some of the recent results on \(L^p\) estimates on the Bergman projection.

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Acknowledgements

I thank Mehmet Çelik, John D’Angelo, Nordine Mir, and Sönmez Şahutoğlu, and the anonymous referee for many useful comments on preliminary versions of this paper.

Funding

This work is supported by NSF (DMS-1659203) and by a Grant from the Simons Foundation (#353525).

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Correspondence to Yunus E. Zeytuncu.

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To the memory of Nick Hanges.

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Zeytuncu, Y.E. A survey of the \(L^p\) regularity of the Bergman projection. Complex Anal Synerg 6, 19 (2020). https://doi.org/10.1007/s40627-020-00056-7

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Keywords

  • Bergman projection
  • \(L^p\) regularity
  • Sobolev regularity

Mathematics Subject Classification

  • Primary 32A25
  • Secondary 32A36