Pseudodifferential operators with smooth symbols and their commutators on weighted Morrey spaces

摘要

In this paper, a local good $$lambda $$ λ inequality for a class of new weight functions which include Muckenhoupt weight functions is established. Applying the local good $$lambda $$ λ inequality and new sharp maximal functions, the authors give a characterization of weighted Morrey spaces. Furthermore, it is proved that the boundedness of pseudodifferential operators with smooth symbols and their commutators on weighted Morrey spaces.