Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO（G） functions on Herz spaces in the setting of homogeneous group. This article ex...Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO（G） functions on Herz spaces in the setting of homogeneous group. This article extends some known results.展开更多
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^...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.展开更多
基金Supported by Chinese Universities Scientific Fund(2009RC0703 of BUPT)the NNSF of China (10871024)
文摘Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO（G） functions on Herz spaces in the setting of homogeneous group. This article extends some known results.
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)
文摘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.
