- February 10,
2012, Friday - 15h00
(Room
P
3.10):
Alexei Karlovich
(Universidade Nova de Lisboa e CEAF, IST)
" Pseudodifferential
Operators on Variable Lebesgue Spaces "
Abstract. 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.
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