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arXiv · 1806.09979

Boundary values of holomorphic distributions in negative Lipschitz classes

Anthony G. O'Farrell
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Abstract

We consider the behaviour at a boundary point of an open subset $U\subset\mathbb{C}$ of distributions that are holomorphic on $U$ and belong to what are called negative Lipschitz classes. The result explains the significance for holomorphic functions of series of Wiener type involving Hausdorff contents of dimension between $0$ and $1$. We begin with a survey about function spaces and capacities that sets the problem in context and reviews the relevant general theory. The techniques used include the construction of a special partition of the identity that may be of independent interest.

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Anthony G. O'Farrell. 2018-06-26. Boundary values of holomorphic distributions in negative Lipschitz classes. https://arxiv.org/abs/1806.09979

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