Pseudodifferential operators and their commutators on Morrey type spaces

Abstract This paper discusses the boundedness of the commutators generated by pseudodifferential operators with Lipschitz functions, and sets up the sufficient condition such that these operators are bounded on classical Morrey spaces and generalized Morrey spaces. This paper also establishes a sufficient condition such that the pseudodifferential operators are bounded from the predual of Morrey spaces into the local predual of Morrey spaces.