摘要
In this paper,it was proved that the commutator H_(β,b)generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from L^(p1)(R^n)to L^(p2)(R^n)if and only if b is a CMO(R^n)function,where 1/p1-1/p2=β/n,1<p1<∞,0≤β<n.Furthermore, the characterization of H_(β,b)on the homogenous Herz space K_q^(α,p)(R^n)was obtained.
In this paper, it was proved that the commutator Hβ,b generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from Lp1(Rn) to Lp2 (Rn) if and only if b is a C(M)O(Rn) function, where 1/p1 - 1/p2 = β/n, 1 ＜ p1 ＜∞, 0 ≤β＜ n. Furthemore,the characterization of Hβ,b on the homogenous Herz space (K)qα,p(Rn) was obtained.
作者
Zun-wei FU~(1,2) Zong-guang LIU~3 Shan-zhen LU~(1+) Hong-bin WANG~3 ~1 School of Mathematical Sciences,Beijing Normal University,Beijing 100875,China
~2 Department of Mathematics,Linyi Normal University,Linyi 276005,China
~3 Department of Mathematics,China University of Mining and Technology (Beijing),Beijing 100083,China
基金
This work was partially supported by the National Natural Science Foundation of China(Grant Nos.10571014,10371080)
the Doctoral Programme Foundation of Institute of Higher Education of China(Grant No.20040027001)
