"Non UBC"@en .
"DSpace"@en .
"Shvartsman, Pavel"@en .
"2014-08-06T22:58:18Z"@en .
"2013-04-24"@en .
"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)\u00E2\u0088\u0088BMO(Rn). Weobtaintheextension F(f) as a fixed point of a certain contractive mapping Tf : L2(Rn) \u00E2\u0086\u0092 L2(Rn).\nThe extension operator f \u00E2\u0086\u0092 F(f) is non-linear, and in general it is not known whether there exists a continuous linear extension operator\nBMO(Rn)|E \u00E2\u0086\u0092 BMO(Rn)\nfor an arbitrary set E.\nIn these talk we present a rather wide family of sets for which such extension op-\nerators 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."@en .
"https://circle.library.ubc.ca/rest/handle/2429/49265?expand=metadata"@en .
"45 minutes"@en .
"video/mp4"@en .
""@en .
"Author affiliation: Technion"@en .
"10.14288/1.0056642"@en .
"eng"@en .
"Unreviewed"@en .
"Vancouver : University of British Columbia Library"@en .
"Banff International Research Station for Mathematical Innovation and Discovery"@en .
"Attribution-NonCommercial-NoDerivs 2.5 Canada"@en .
"http://creativecommons.org/licenses/by-nc-nd/2.5/ca/"@en .
"Faculty"@en .
"BIRS Workshop Lecture Videos (Banff, Alta)"@en .
"Mathematics"@en .
"Functional analysis"@en .
"Real functions"@en .
"Extensions of BMO-functions and fixed points of contractive mappings in L2, II"@en .
"Moving Image"@en .
"http://hdl.handle.net/2429/49265"@en .