Characterization of boundedness of some commutators of fractional maximal functions in terms of p-adic vector spaces

This paper gives some characterizations of the boundedness of the maximal or non-linear commutator of the p-adic fractional maximal operator Mαᵖ with the symbols belong to the p-adic BMO spaces on (variable) Lebesgue spaces and Morrey spaces over p-adic field, by which some new characterizations of BMO functions are obtained in the p-adic field context. Meanwhile, some equivalent relations between the p-adic BMO norm and the p-adic (variable) Lebesgue or Morrey norm are given. Bibliography: 35 titles.