TY - ELEC
AU - Shvartsman, Pavel
PY - 2013
TI - Extensions of BMO-functions and fixed points of contractive mappings in L2, II
LA - eng
M3 - Moving Image
AB - 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.
N2 - 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.
UR - https://open.library.ubc.ca/collections/48630/items/1.0056642
ER - End of Reference