论文标题
截短的Beurling操作员的加权Sobolev估计值
Weighted Sobolev estimates of the truncated Beurling operator
论文作者
论文摘要
给定一个有界的平面域$ d $，带有$ W^{k+1，\ infty} $边界，$ k \ in \ mathbb z^+$，在a_p，1 <p <\ infty $中，我们表明，相应的截断的beurling变换是一个有界的操作员，是发送$ w^^^{k，p^，p^n ofterling trunculling thrunculling变换。还获得了其他Cauchy型积分的加权Sobolev估计值。
Given a bounded planar domain $D$ with $W^{k+1, \infty}$ boundary, $ k\in \mathbb Z^+$, and a weight $μ\in A_p, 1<p<\infty$, we show that the corresponding truncated Beurling transform is a bounded operator sending $W^{k, p}(D, μ)$ into itself. Weighted Sobolev estimates for other Cauchy-type integrals are also obtained.
