Noncommutative pseudo-differential operators

Abstract:

We will introduce our recent work on pseudo-differential operators in noncommutative setting. We focus on two main topics: symbolic calculus and regularities on function spaces. We describe the composition of two pseudo-differential operators, and get the regularities on various function spaces: Sobolev, Besov, Hardy, Triebel-Lizorkin. We will also mention the overlap between our work and those done by Ponge, Junge, Parcet, etc.