Endpoint maximal and smoothing estimates for Schrödinger equations

Abstract

For α > 1 we consider the initial value problem for the dispersive equation i∂tu + (–Δ)α/2u = 0. We prove an endpoint Lp inequality for the maximal function with initial values in Lp-Sobolev spaces, for p ∈ (2 + 4/(d + 1), ∞). This strengthens the fixed time estimates due to Fefferman and Stein, and Miyachi. As an essential tool we establish sharp Lp space-time estimates (local in time) for the same range of p.

Locations

• CiteSeer X (The Pennsylvania State University) - View - PDF
• Journal für die reine und angewandte Mathematik (Crelles Journal) - View