Functional Analysis and Applications Seminar 

16/12/2005, 15:00 — 16:00 — Room P3.10, Mathematics Building
Yuri Karlovich, Universidad Autónoma del Estado de Morelos, México

A weighted analogue of the Carleson-Hunt theorem and new classes of pseudodifferential operators

Applying a weighted analogue of the Carleson-Hunt theorem on almost everywhere convergence, we study the boundedness and compactness of pseudodifferential operators with symbols that are bounded measurable functions with respect to the spatial variable and functions of bounded variation with respect to the dual variable. Replacement of absolutely continuous functions of bounded variation by arbitrary functions of bounded variation allows us to study essentially more general classes of pseudodifferential operators. A symbol calculus and a Fredholm theory for new classes of pseudodifferential operators with non-regular symbols are constructed. In particular, we study pseudodifferential operators with symbols admitting discontinuities of first kind with respect to spatial and dual variables that generate non-commutative algebras of Fredholm symbols.