Boundary Behavior of Functions Representable by Weighted Koppelman Type Integral and Related Hartogs Phenomenon

Abstract

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.