p-Adic域上分数次Hardy算子多线性交换子有界性

Boundness of Multilinear Commutaors of Fractional Hardy Operators over p-Adic Field

在p-adic域上的Lebesgue空间Lr(Qpn)和Herz空间Kra,q(Qpn)上建立了分数次Hardy算子与BMO(Qpn)函数生成的多线性交换子Hβ,bp和Hβ,bp,*的有界性.作为特例,得到了Hardy算子的交换子H0,bp和,H0,bp,*的有界性.

In this paper, the boundedness of the multilinear commutators Hβ,b-^p and Hβ,b-^p＊ generated by fractional Hardy operator and BMO（Q%） function are established on the Lebesgue space Lr（Qp^N）and Herz space Kr^α,q（Qp^n） over p-adic field. Furthermore, the commutator of Hardy operator H0,b-^p and H0,b-^p are also considered as a special case.