Analysis Seminar - 26/3/2014

Wednesday, 26 March 2014, 2:00 p.m.

Lecturer: Oleksiy Karlovych, CMA/FCT-UNL

Title: "Pseudodifferential operators on Banach function spaces".

Local: Room 1.5, Edifício VII
Faculdade de Ciências e Tecnologia, Quinta da Torre, Caparica

 

Abstract: We prove a boundedness result for pseudodifferential operators with certain Hormander symbols on Banach function spaces. This class of spaces includes Lebesgue, Orlicz, rearrangement-invariant spaces, as well as, variable Lebesgue spaces. Further we present a sufficient condition for the Fredholmness (=invertibility modulo the ideal of compact operators) of pseudodifferential operators with slowly oscillating symbols on variable Lebesgue spaces with exponents beyond the class of log-Holder continuous exponents. Both theorems generalize pioneering results by Rabinovich and Samko for variable Lebesgue spaces with log-Holder continuous exponents.