Monatshefte für Mathematik

, Volume 109, Issue 2, pp 135–143 | Cite as

Radial functions and regularity of solutions to the Schrödinger equation

  • Elena Prestini
Article

Abstract

Letf be a radial function and setT*f(x)=sup0<t<1 |Ttf(x)|, x ∈ ℝn, n≥2, where(Ttf)^ (ξ)=eit|ξ|a\(\hat f\) (ξ),a > 1. We show that, ifB is the ball centered at the origin, of radius 100, then\(\int\limits_B {|T^ * f(x)|} dx \leqslant c(\int {|\hat f(\xi )|^2 (l + |\xi |^s )ds} )^{1/2} \) if and only ifs≥1/4.

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Elena Prestini
    • 1
  1. 1.Dipartimento di MatematicaUniversità di MilanoMilanoItaly

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