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Title	Extensions of BMO-functions and fixed points of contractive mappings in L2, I
Creator	Shvartsman, Pavel
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2013-04-24
Description	Let E be a closed subset of Rn of positive Lebesgue measure. We discuss a constructive algorithm which to every function f defined on E assigns its almostoptimalextensiontoafunctionF(f)∈BMO(Rn). Weobtaintheextension F(f) as a fixed point of a certain contractive mapping Tf : L2(Rn) → L2(Rn). The extension operator f → F(f) is non-linear, and in general it is not known whether there exists a continuous linear extension operator BMO(Rn)|E → BMO(Rn) for an arbitrary set E. In these talk we present a rather wide family of sets for which such extension op- erators exist. In particular, this family contains closures of domains with arbitrary internal and external cusps. The proof of this result is based on a solution to a similar problem for spaces of Lipschitz functions defined on subsets of a hyperbolic space.
Extent	54 minutes
Subject	Mathematics Functional analysis Real functions
Type	Moving Image
FileFormat	video/mp4
Language	eng
Notes	Author affiliation: Technion
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2014-08-06
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivs 2.5 Canada
DOI	10.14288/1.0056641
URI	http://hdl.handle.net/2429/49264
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/2.5/ca/
AggregatedSourceRepository	DSpace

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