Abstract
Letf be a radial function and setT * f(x)=sup0<t<1 |T t f(x)|, x ∈ ℝn, n≥2, where(Tt f)^ (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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Prestini, E. Radial functions and regularity of solutions to the Schrödinger equation. Monatshefte für Mathematik 109, 135–143 (1990). https://doi.org/10.1007/BF01302933
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DOI: https://doi.org/10.1007/BF01302933