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.
