2009/05/15 by Pavel Shvartsman, Shvartsman, Pavel
Mathematics · #46E35 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46E35
paper · pdf · doi:10.48550/arxiv.0905.2602
43 pages
arxiv created 2009/05/15 · openalex publication_date 2009/05/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a variant of the Whitney extension problem for the space CkΛmω(Rn) of functions whose partial derivatives of order k satisfy the generalized Zygmund condition. We identify CkΛmω(Rn) with a space of Lipschitz mappings from a metric space (Rn+1+,ρω) supplied with a hyperbolic metric ρω into a metric space (\cal Pk+m-1× Rn+1+, dω) of polynomial fields on Rn+1+ equipped with a hyperbolic-type metric dω. This identification allows us to reformulate the Whitney problem for CkΛmω(Rn) as a Lipschitz selection problem for set-valued mappings from (Rn+1+,ρω) into a certain family of subsets of \cal Pk+m-1× Rn+1+.