P-adic weak central Morrey spaces on differential forms

Abstract

. In this article, the theory of differential forms on R n was extended to the fi led Q np of p -adic numbers. The imbedding inequalities for differential forms were derived on Q np . Then, we show the de fi nitions of p -aidc weak central Morrey spaces and p -adic λ -central BMO spaces on differential forms. The boundedness of Hardy operator and its adjoint operator were given in the new space. Finally, we give the characterization of the two operators in p -adic λ -central BMO spaces by using imbedding inequalities on differential forms.