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Norm Estimates for the Bergman and Cauchy–Szegö Projections Over the Siegel Upper Half-Space

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Abstract

We obtain several estimates for the \(L^p\) operator norms of the Bergman and Cauchy–Szegö projections over the the Siegel upper half-space. As a by-product, we also determine the precise value of the \(L^p\) operator norm of a family of integral operators over the Siegel upper half-space.

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Acknowledgements

The author is indebted to Lifang Zhou for correcting two errors in an earlier version of the paper, and to Guangbin Ren and Xieping Wang for many helpful comments.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, Anhui, People’s Republic of China

    Congwen Liu

  2. Wu Wen-Tsun Key Laboratory of Mathematics, Chinese Academy of Sciences, USTC, Hefei, People’s Republic of China

    Congwen Liu

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  1. Congwen Liu
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Correspondence to Congwen Liu.

Additional information

Communicated by Edward B. Saff.

This work was supported by the National Natural Science Foundation of China Grants 11571333, 11471301.

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Liu, C. Norm Estimates for the Bergman and Cauchy–Szegö Projections Over the Siegel Upper Half-Space. Constr Approx 48, 385–413 (2018). https://doi.org/10.1007/s00365-017-9390-6

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  • DOI: https://doi.org/10.1007/s00365-017-9390-6

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