Functional Analysis and Applications Seminar 

10/02/2012, 15:00 — 16:00 — Room P3.10, Mathematics Building
Alexei Karlovich, Universidade Nova de Lisboa e CEAF, IST

Pseudodifferential Operators on Variable Lebesgue Spaces

We show that a pseudodifferential operator with symbol in the Hörmander class $S_{r,d}^{n(r-1)}$ is bounded on a reflexive variable Lebesgue space for a wide range of parameters r and d whenever the Hardy-Littlewood maximal operator is bounded. Further we prove a sufficient condition for the Fredholmness of a pseudodifferential operator with a symbol that slowly oscillates in the first variable and belongs to $S_{1,0}^0$. Both theorems generalize pioneering results by Rabinovich and Samko (IEOT, 2008) obtained for globally log-Hölder continuous variable exponents. This is a joint work with Ilya Spitkovsky.