One sided extendability and p-continuous analytic capacities

2016/06/17 by Bolkas, E., Nestoridis, V., Panagiotis, C. +1
#30C85 #30H05 #53A04 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1606.05443

Abstract

Using complex methods combined with Baire's Theorem we show that one-sided extendability, extendability and real analyticity are rare phenomena on various spaces of functions in the topological sense. These considerations led us to introduce the p-continuous analytic capacity and variants of it, p ∈ \ 0, 1, 2, ⋯ \ ∪ \ ∞ \, for compact or closed sets in ℂ. We use these capacities in order to characterize the removability of singularities of functions in the spaces A^p.

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