Lattice Homomorphisms between Sobolev spaces,   Markus Biegert,   University of Ulm (Germany),  Tue, 3 March, 2009,   11:30 a.m. A-233


In this talk we will present an abstract theorem which allows one to deduce that a lattice homomorphism between certain function spaces can be represented as a weighted composition operator.

As an application of this abstract theorem, we will show that every lattice homomorphism T:W0[1,p](Ω_1) -->W0[1,q](Ω_2) has the form T(u)(y) = u(ξ(y))g(y) quasi everywhere on Ω_2 where ξ:Ω_2 -->Ω_1 and g:Ω_2 --> [0, ∞).