Functional Analysis and Applications Seminar 

17/12/2002, 14:00 — 15:00 — Room P5, Mathematics Building
Yuri Karlovich, Universidad Autónoma del Estado de Morelos, México

Pseudodifferential Operators and Their Applications

The talk is devoted to a symbol calculus for Banach algebras of pseudodifferential operators (PDO's) with slowly oscillating data and their applications to an interpolation theorem for singular integral operators on weighted Lebesgue spaces and to the calculation of local spectra for singular integral operators with shifts and slowly oscillating data on Lebesgue spaces with Muckenhoupt weights over Carleson curves. The study is based on the Carleson-Hunt theorem on almost everywhere convergence and its applications to the boundedness of PDO's, on the techniques of oscillatory integrals, and on the theory of Mellin PDO's with slowly oscillating symbols.