Abstract
In this paper, we generalize to homogeneous Siegel domains of second kind the L p-continuity properties of the Bergman projection. Precisely, we give an improvement of the index p using Fourier analysis as in the case of convex homogeneous tube type domains (Nana and Trojan in Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) X:477–511, 2011).
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Notes
If there is k∈{1,…,r} such that \(\nu_{k}\leq\frac{m_{k}+b_{k}}{2}\), then \(A_{\nu}^{p}(D)=\{0\}\). (See [3, Corollary II.3].)
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Communicated by Fulvio Ricci.
The author is very grateful to D. Békollé for his advices and suggestions. Special thanks to the referee for all remarks and suggestions made to improve the quality of the paper.
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Nana, C. L p,q-Boundedness of Bergman Projections in Homogeneous Siegel Domains of Type II. J Fourier Anal Appl 19, 997–1019 (2013). https://doi.org/10.1007/s00041-013-9280-7
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DOI: https://doi.org/10.1007/s00041-013-9280-7