Per Sjölin

Applications of Fourier Analysis in Homogenization of the Dirichlet Problem: L p Estimates

AbstractLet uɛ be a solution to the system

Estimates of averages of Fourier transforms with respect to general measures

\rm div(A_\varepsilon(x)\nabla u_\varepsilon(x)) = 0 \quad\text{in}\, D,\quad u_\varepsilon(x) = g(x,x/\varepsilon)\quad\text{on} \,\partial\, D,

A note on Schrödinger maximal operators with a complex parameter

div(Aε(x)∇uε(x))=0inD,uε(x)=g(x,x/ε)on∂D,where

Heisenberg uniqueness pairs and a theorem of Beurling and Malliavin

{D \subset \mathbb{R}^d (d \geqq 2)}

Global maximal estimates for solutions to the Schrödinger equation

D⊂Rd(d≧2), is a smooth uniformly convex domain, and g is 1-periodic in its second variable, and both Aɛ and g are sufficiently smooth. Our results in this paper are twofold. First we prove Lp convergence results for solutions of the above system and for the non oscillating operator