Non UBC
DSpace
Shvartsman, Pavel
2014-08-06T22:58:18Z
2013-04-24
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)âˆˆBMO(Rn). Weobtaintheextension F(f) as a fixed point of a certain contractive mapping Tf : L2(Rn) â†’ L2(Rn).
The extension operator f â†’ F(f) is non-linear, and in general it is not known whether there exists a continuous linear extension operator
BMO(Rn)|E â†’ 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.
https://circle.library.ubc.ca/rest/handle/2429/49265?expand=metadata
45 minutes
video/mp4
Author affiliation: Technion
10.14288/1.0056642
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivs 2.5 Canada
http://creativecommons.org/licenses/by-nc-nd/2.5/ca/
Faculty
BIRS Workshop Lecture Videos (Banff, Alta)
Mathematics
Functional analysis
Real functions
Extensions of BMO-functions and fixed points of contractive mappings in L2, II
Moving Image
http://hdl.handle.net/2429/49265