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arXiv · 2210.02619

Optimal Sobolev regularity of $\bar\partial$ on the Hartogs triangle

Yifei Pan·Yuan Zhang
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Abstract

In this paper, we show that for each $k\in \mathbb Z^+, p>4$, there exists a solution operator $\mathcal T_k$ to the $\bar\partial$ problem on the Hartogs triangle that maintains the same $W^{k, p}$ regularity as that of the data. According to a Kerzman-type example, this operator provides solutions with the optimal Sobolev regularity.

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Yifei Pan, Yuan Zhang. 2022-10-06. Optimal Sobolev regularity of $\bar\partial$ on the Hartogs triangle. https://arxiv.org/abs/2210.02619

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