In the present paper we study the boundary behavior of a weighted Koppelman type integral with a specific choice of weight for a function \(\phi \) that is integrable on a bounded domain \(D\subset \mathbb {C}^n\) and is continuous on its \(\mathcal {C}^1\)-boundary. Applying the above results, we derive a variation of Hartogs phenomena about the holomorphicity of a function \(\phi \) which is integrable in a D and continuous on \(\partial D\), provided that it satisfies, in some sense, a stronger version of “one-dimensional holomorphic continuation property” along any complex line meeting the domain.

中文翻译：

---

加权Koppelman型积分和相关Hartogs现象表示的函数的边界行为。

在本论文中，我们用一个特定的选择权重的一个函数研究了加权的Koppelman型积分的边界行为\（\披\）即积上的有界区域\（d \子集\ mathbb {C} ^ N \ ），并且在\（\ mathcal {C} ^ 1 \）边界上是连续的。应用以上结果，我们得出关于函数\（\ phi \）的全纯性的Hartogs现象的变体，该函数在D中可积分并且在\（\ partial D \）上连续，只要在某种意义上满足，沿满足该域的任何复杂线的“一维全同连续性”的更强版本。