Capacities of compact sets in linear subspaces of Rⁿ

Tord Sjödin

Vol. 78 (1978), No. 1, 261–266

DOI: 10.2140/pjm.1978.78.261

Abstract

We consider two types of spaces, the Bessel potential spaces L_α^p(Rⁿ) and the Besov spaces Λ_α^p(Rⁿ), α > 0, 1 < p < ∞. Associated in a natural way with these spaces are classes of exceptional sets. We characterize the exceptional sets for Λ_α^p(Rⁿ) by an extension property for continuous functions and prove an inequality between Bessel and Besov capacities.

Mathematical Subject Classification 2000

Primary: 31B10

Secondary: 46E35

Milestones

Received: 8 October 1976

Published: 1 September 1978