Weighted Sobolev estimates of the truncated Beurling operator
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866910337054277632 |
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| author | Pan, Yifei Zhang, Yuan |
| author_facet | Pan, Yifei Zhang, Yuan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_02613 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Weighted Sobolev estimates of the truncated Beurling operator Pan, Yifei Zhang, Yuan Complex Variables Primary 30E20, Secondary 42B37, 46E35 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. |
| title | Weighted Sobolev estimates of the truncated Beurling operator |
| topic | Complex Variables Primary 30E20, Secondary 42B37, 46E35 |
| url | https://arxiv.org/abs/2210.02613 |