A strong type $(2,\,2)$ estimate for a maximal operator associated to the Schrödinger equation

Carlos E. Kenig, Alberto Ruiz
1983 Transactions of the American Mathematical Society  
Let T*f(x) = sup/>0|7;/(x)|, where (T,f)~(t) = e',|í|2/(í)/|í|'/4-We show that, given any finite interval /, j,\ T*f\2 dx < C, fR\f(x)\2 dx, and that the above inequality is false with 2 replaced by any p < 2. This maximal operator is related to solutions of the Schrödinger equation.
doi:10.1090/s0002-9947-1983-0712258-4 fatcat:xog3o2venfbvdezakcdu4sjefy