Functional Analysis and Applications Seminar 

14/01/2005, 15:00 — 16:00 — Room P3.10, Mathematics Building
Yuri Karlovich, Universidad Autónoma del Estado de Morelos, México

Pseudodifferential Operators with Non-Regular Symbols

The talk is devoted to studying pseudodifferential operators of zero order with non-regular symbols that satisfy a Hölder condition with respect to the spatial variable and are uniformly bounded continuous functions of bounded total variation on dyadic intervals with respect to the dual variable. Applying the Littlewood-Paley theory and previous results on pseudodifferential operators, we obtain conditions for the boundedness and compactness of such pseudodifferential operators on Lebesgue spaces over the real line. We construct a symbol calculus and a Fredholm theory for pseudodifferential operators with non-regular symbols that additionally slowly oscillate at infinity with respect to both variables.