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Dyadic decomposition of convex domains of finite type and applications

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Abstract

In this paper, we introduce a dyadic structure on convex domains of finite type via the so-called dyadic flow tents. This dyadic structure allows us to establish weighted norm estimates for the Bergman projection P on such domains with respect to Muckenhoupt weights. In particular, this result gives an alternative proof of the \(L^p\) boundedness of P. Moreover, using extrapolation, we are also able to derive weighted vector-valued estimates and weighted modular inequalities for the Bergman projection.

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Acknowledgements

The authors would like to thank Brett Wick for insightful discussion and helpful comments which improved the current version of this paper.

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Authors and Affiliations

  1. University of Wisconsin-Madison, 480 Lincoln Drive, Madison, WI, 53706, USA

    Chun Gan

  2. Department of Mathematics, Purdue University, 150 N. University St., West Lafayette, IN, 47907, USA

    Bingyang Hu

  3. Mathematical Institute, Andrew Wiles Building, University of Oxford, Woodstock Rd, Oxford, OX2 6GG, UK

    Ilyas Khan

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  1. Chun Gan
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  2. Bingyang Hu
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Correspondence to Bingyang Hu.

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Gan, C., Hu, B. & Khan, I. Dyadic decomposition of convex domains of finite type and applications. Math. Z. 301, 1939–1962 (2022). https://doi.org/10.1007/s00209-022-02984-y

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