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arXiv · 2001.07200

Dyadic decomposition of convex domains of finite type and applications

Chun Gan·Bingyang Hu·Ilyas Khan
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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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Chun Gan, Bingyang Hu, Ilyas Khan. 2020-01-20. Dyadic decomposition of convex domains of finite type and applications. https://arxiv.org/abs/2001.07200

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