论文标题
Bergman和Cauchy-szegő在域上投影的加权端点边界几乎平滑度
Weighted endpoint bounds for the Bergman and Cauchy-Szegő projections on domains with near minimal smoothness
论文作者
论文摘要
我们研究伯格曼投影，$ \ Mathcal {b} $和Cauchy-Szegő投影，$ \ Mathcal {S} $，在具有最小平滑度的有限域上。我们证明$ \ nathcal {b} $具有相对于加权措施的弱型$（1,1）$，假设基础域具有强烈的pseudoconvex，具有$ c^4 $界限，重量且重量满足$ b_1 $的条件，并且满足$ \ \ \ ntive $ c^3 $ c^3 $ c^3 $ c^3 $ c^3 $ c^3 33 健康）状况。我们还以$ \ Mathcal {B} $和$ \ Mathcal {s} $在其各自的设置中以冠冕获得了加权的Kolmogorov和加权的Zygmund不等式。
We study the Bergman projection, $\mathcal{B}$, and the Cauchy-Szegő projection, $\mathcal{S}$, on bounded domains with near minimal smoothness. We prove that $\mathcal{B}$ has the weak-type $(1,1)$ property with respect to weighted measures assuming that the underlying domain is strongly pseudoconvex with $C^4$ boundary and the weight satisfies the $B_1$ condition, and the same property for $\mathcal{S}$ on domains with $C^3$ boundaries and weights satisfying the $A_1$ condition. We also obtain weighted Kolmogorov and weighted Zygmund inequalities for $\mathcal{B}$ and $\mathcal{S}$ in their respective settings as corollaries.
