The Mikhlin-H\"ormander multiplier theorem: some recent developments

Series: 
Analysis Seminar
Wednesday, October 10, 2018 - 1:55pm
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
University of Missouri
,  
Organizer: 
In this talk I will discuss the Mikhlin-H\"ormander multiplier theorem for $L^p$ boundedness of Fourier multipliers in which the multiplier belongs to a fractional Sobolev space with smoothness $s$. I will show that this theorem does not hold in the limiting case $|1/p - 1/2|=s/n$. I will also present a sharp variant of this theorem involving a space of Lorentz-Sobolev type. Some of the results presented in this talk were obtained in collaboration with Loukas Grafakos.