On Some Degenerate Pseudodifferential Operators

Abstract

A new class of degenerate pseudodifferential operators with a variable symbol depending on a complex parameter is investigated. Pseudodifferential operators are constructed by applying a special integral transform. Theorems on the composition and boundedness of these operators in special weighted spaces are proved. The behavior of these operators on hyperplanes of degeneration is investigated. Theorems on the commutation of these operators with differentiation operators are established. An adjoint operator is constructed, and an analogue of Gårding’s inequality for degenerate pseudodifferential operators is proved.