"Sharp estimates for Fourier multipliers"

Abstract: A Fourier multiplier is an operator that acts on a given function by altering its frequency via multiplication.  Precisely, a Fourier multiplier operator is given by composition of the following three operators: the Fourier transform, multiplication by a bounded function, and the inverse Fourier transform. The problem of finding sharp sufficient conditions for functions to define Fourier multiplier operators bounded on different function spaces is of central importance in harmonic analysis. Obtaining such conditions is the best one can expect as there is no good characterization of boundedness of multipliers, even on spaces as simple as $L^p$. Results of this sort usually bear the name "multiplier theorems''.
In this talk, I will review the classical multiplier theorems of H\"ormander and Marcinkiewicz and present sharp versions of these results. I will also discuss some sharp bilinear multiplier theorems.

Host: Brett Wick

Tea will be served @ 3:45 in room 200