Monatshefte für Mathematik

, Volume 109, Issue 2, pp 135–143

Radial functions and regularity of solutions to the Schrödinger equation

Authors

  • Elena Prestini
    • Dipartimento di MatematicaUniversità di Milano
Article

DOI: 10.1007/BF01302933

Cite this article as:
Prestini, E. Monatshefte für Mathematik (1990) 109: 135. doi:10.1007/BF01302933
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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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© Springer-Verlag 1990