L-p-Boundedness of Wave Operators for 2D Schrodinger Operators with Point Interactions

摘要

For two dimensional Schrodinger operator H with point interactions, we prove that wave operators of scattering for the pair (H, H-0), H-0 being the free Schrodinger operator, are bounded in the Lebesgue space L-p(R-2) for 1 < p < infinity if and only if there are no generalized eigenfunctions of Hu(x) = 0 which satisfy u(x) = C vertical bar x vertical bar(-1) + o(vertical bar x vertical bar(-1)) as vertical bar x vertical bar -> infinity, C not equal 0. Otherwise they are bounded for 1 < p <= 2 and unbounded for 2 < p < infinity.