论文标题
伯格曼投影对光滑无界蠕虫域的不规则性
Irregularity of the Bergman projection on smooth unbounded worm domains
论文作者
论文摘要
在这项工作中，我们考虑了$ \ mathbb c^2 $中的平滑无限的蠕虫域$ \ Mathcalz_λ$，并表明伯格曼投影在sobolev spaces $ h^{s，p}（\ mathcal z_月份）$，$ p \ in（1，\ infty）$，$ s $ septor的$ h^{s，p}（\ mathcalz_λ）$，$ s \ ge0 tes tes tes tes tos tes to a a a a ge0 $p_λ：h^{s，p}（\ Mathcalz_λ）\ to H^{s，p}（\ MathcalZ_λ）$时$ s> 0 $或$ p \ neq2 $。在非平滑未结合的蠕虫的情况下，已知相同的不规则性。改进的结果表明，投影的不规则性不是边界不规则性的结果，而是蠕虫域的无限绕组。
In this work we consider smooth unbounded worm domains $\mathcal Z_λ$ in $\mathbb C^2$ and show that the Bergman projection, densely defined on the Sobolev spaces $H^{s,p}(\mathcal Z_λ)$, $p\in(1,\infty)$, $s\ge0$, does not extend to a bounded operator $P_λ:H^{s,p}(\mathcal Z_λ)\to H^{s,p}(\mathcal Z_λ)$ when $s>0$ or $p\neq2$. The same irregularity was known in the case of the non-smooth unbounded worm. This improved result shows that the irregularity of the projection is not a consequence of the irregularity of the boundary but instead of the infinite windings of the worm domain.
