One sided extendability and p-continuous analytic capacities

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, $p\in \{0,1,2,\cdots \}\cup \{\infty \}$, for compact or closed sets in $\mathbb{C}$. We use these capacities in order to characterize the removability of singularities of functions in the spaces $A^p$.

Corrected some typos and added some new results

References in corpus (2)

• Non extendability from any side of the domain of definition as a generic property of smooth or simply continuous functions on an analytic curve
• Arc length as a conformal parameter for locally analytic curves

Cited by in corpus (1)

• Holomorphic extendability in ${\mathbf{C}}^n$ as a rare phenomenon