A CALDERON-ZYGMUND EXTENSION THEOREM FOR ABSTRACT SOBOLEV SPACES

摘要

It is shown that if the Boyd indices of the rearrangement invariant Banach function space L_ρ (R~n) are strictly between 0 and 1, ρ is an absolutely continuous function norm, Ω is a domain from R~n satisfying the restricted cone condition, denoting by ω the restriction of ρ to Ω, there exists an extension operator for the abstract Sobolev space W~mL_ω(Ω). This is a generalization to abstract Sobolev spaces of a result obtained by de Souza for Orlicz-Sobolev spaces.