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arXiv · 2210.02613

Weighted Sobolev estimates of the truncated Beurling operator

Yifei Pan·Yuan Zhang
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Abstract

Given a bounded planar domain $D$ with $W^{k+1, \infty}$ boundary, $ k\in \mathbb Z^+$, and a weight $\mu\in A_p, 1<p<\infty$, we show that the corresponding truncated Beurling transform is a bounded operator sending $W^{k, p}(D, \mu)$ into itself. Weighted Sobolev estimates for other Cauchy-type integrals are also obtained.

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Yifei Pan, Yuan Zhang. 2022-10-06. Weighted Sobolev estimates of the truncated Beurling operator. https://doi.org/10.1112/blms.12926

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