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.
