Algebras of singular integral operators with shifts
The talk is devoted to studying pseudodifferential operators with
non-regular symbols and their applications to singular integral
operators with shifts. Algebras of singular integral operators with
discrete subexponential groups of shifts are studied on weighted
Lebesgue spaces provided that the contour, the weight, the
coefficients and the shifts are slowly oscillating. Applying a
local-trajectory method and a theory of Mellin pseudodifferential
operators with non-regular symbols, we construct Fredholm symbol
calculi for the mentioned algebras of singular integral operators
with shifts and establish corresponding Fredholm criteria.
