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Mathematische Annalen

, Volume 374, Issue 1–2, pp 395–427 | Cite as

Lebesgue mixed norm estimates for Bergman projectors: from tube domains over homogeneous cones to homogeneous Siegel domains of type II

  • David BékolléEmail author
  • Jocelyn Gonessa
  • Cyrille Nana
Article
  • 55 Downloads

Abstract

In this paper, the weight functions are fundamental compound functions of the homogeneous cone. First, we use the recent Bourgain-Demeter \(l^2\)-decoupling theorem to obtain the optimal weighted Lebesgue mixed norm estimates for weighted Bergman projectors on tube domains over Lorentz cones. This settles a conjecture of D. Debertol. Secondly, we present a transference principle of weighted Lebesgue mixed norm estimates for weighted Bergman projectors from tube domains over homogeneous cones to homogeneous Siegel domains of type II associated to the same cones. So results of C. Nana for homogeneous Siegel domains of type II can be deduced from earlier results of C. Nana and B. Trojan for tube domains over homogeneous cones. Combining our two theorems, we improve these estimates for homogeneous Siegel domains of type II associated with Lorentz cones, e.g. the Pyateckii-Shapiro Siegel domain of type II.

Mathematics Subject Classification

Primary 32A25 32M15 46B30 Secondary 46E22 

Notes

Acknowledgements

The authors wish to express their gratitude to the referee for his (her) careful reading of the manuscript, his (her) criticisms and suggestions which led to the optimal statement of Theorem 2.3. In particular, he (she) suggested the present version of the assertion (2) of Theorem 6.8. The authors also thank Aline Bonami and Gustavo Garrigós for valuable discussions.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceUniversity of NgaoundéréNgaoundéréCameroon
  2. 2.Département de Mathématiques et IndormatiqueFaculté des SciencesBanguiRépublique Centrafricaine
  3. 3.Department of Mathematics, Faculty of ScienceUniversity of BueaBueaCameroon

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