2018/06/26 by Anthony G. O'Farrell, O'Farrell, Anthony G.
Mathematics · #30E25 #30H99 #46F20 #46J10 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:30E25 #msc:30H99 #msc:46F20 #msc:46J10
paper · pdf · doi:10.48550/arxiv.1806.09979
28 pages
arxiv created 2019/02/07 · arxiv updated 2019/02/08
We consider the behaviour at a boundary point of an open subset U⊂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.