A multiplier theorem using the Schechterʹs method of interpolation Original Research Article

Let m be a measurable bounded function and let us assume that there exists a bounded functions S so that m(ξ)S(ξ)it−1 is a Fourier multiplier on Lp uniformly in t∈R. Then, using the analytic interpolation theorem of Stein, one can show that necessarily m is a Lp multiplier. The purpose of this work is to show that under the above conditions, it holds that, for every k∈N, m(log S)k∈Mp. The technique is based on the Schechterʹs interpolation method.