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arXiv · 1303.5220

Integrating holomorphic $L^1$-functions

A. -K. Herbig
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Abstract

Let $\Omega\Subset\mathbb{C}^{n}$ be a domain with smooth boundary, $k\in\mathbb{N}$. It is shown that the integral of a holomorphic function in $L^1(\Omega)$ may be represented as the integral of this function against a smooth function vanishing to order $k-1$ on $b\Omega$. An application for a smoothing property of the Bergman projection for conjugate holomorphic functions is given.

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A. -K. Herbig. 2013-03-21. Integrating holomorphic $L^1$-functions. https://arxiv.org/abs/1303.5220

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