Smoothing and dispersive estimates for ID Schrodinger equations with BV coefficients and applications

We prove smoothing estimates for Schrodinger equations i partial derivative(t)phi + partial derivative(x)(a(x)partial derivative(x)phi) = 0 with a(x) is an element of BV, real and bounded from below. We then bootstrap these estimates to obtain optimal Strichartz and maximal function estimates, all of which turn out to be identical to the constant coefficient case. We also provide counterexamples showing a c BV to be in a sense a minimal requirement. Finally, we provide an application to sharp well-posedness for a generalized Benjamin-Ono equation. (c) 2006 Elsevier Inc. All rights reserved.