The Whitney extension problem for Zygmund spaces and Lipschitz selections in hyperbolic jet-spaces

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dc.creatorShvartsman, Pavel
dc.date2009-05-15
dc.date.accessioned2026-07-07T13:15:40Z
dc.date.available2026-07-07T13:15:40Z
dc.descriptionWe study a variant of the Whitney extension problem for the space $C^kΛ^m_ω(R^n)$ of functions whose partial derivatives of order $k$ satisfy the generalized Zygmund condition. We identify $C^kΛ^m_ω(R^n)$ with a space of Lipschitz mappings from a metric space $(R^{n+1}_+,ρ_ω)$ supplied with a hyperbolic metric $ρ_ω$ into a metric space $({\cal P}_{k+m-1}\times R^{n+1}_+, d_ω)$ of polynomial fields on $R^{n+1}_+$ equipped with a hyperbolic-type metric $d_ω$. This identification allows us to reformulate the Whitney problem for $C^kΛ^m_ω(R^n)$ as a Lipschitz selection problem for set-valued mappings from $(R^{n+1}_+,ρ_ω)$ into a certain family of subsets of ${\cal P}_{k+m-1}\times R^{n+1}_+$.
dc.description43 pages
dc.identifierhttps://arxiv.org/abs/0905.2602
dc.identifierhttp://arxiv.org/abs/0905.2602
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/230543
dc.subjectFunctional Analysis
dc.subject46E35
dc.titleThe Whitney extension problem for Zygmund spaces and Lipschitz selections in hyperbolic jet-spaces
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