A local smoothing estimate for the Schrödinger equation

• Autores: Keith M. Rogers
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 219, Nº 6, 2008, págs. 2105-2122
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.08.008
• Texto completo no disponible (Saber más ...)
• Resumen

  • We show that the Schrödinger operator eit? is bounded from to for all a>2n(1/2-1/q)-2/q and q2+4/(n+1). This is almost sharp with respect to the Sobolev index. We also show that the Schrödinger maximal operator sup0s0 if and only if it is bounded from to when s>2s0. A corollary is that sup03/4.