非齐型空间中一类满足Hrmander条件的Marcinkiewicz交换子估计

Estimates for Commtators of Marcinkiewicz Integrals with Hrmander-Type Condition in Non-Homogeneous Spaces

记μ为R^d上的非负Radon测度,且仅满足对固定的C_0>0和n∈(0,d],及所有的x∈R^d和r>0,μ(B(x,r))≤C_0r^n.作者建立了一类核函数满足H(o|¨)rmander条件的Marcinkiewicz积分与Lip_β(μ)(0<β)函数生成的交换子由L^p(μ)到L^q(μ),由L^p(μ)到Lip_(β-n/p)(μ)及L^(n/β)(μ)到RBMO(μ)有界.部分结论对经典Marcink(?)ewicz积分也是新的.

Let μ be a positive Radon measure on R^d which may be non doubling. The only condition that μ must satisfy is μ（B（x, r）） ≤ Cr^n for all x ∈R^d , r 〉 0 and some fixed n E （0, d]. In this paper, the authors establish the boundedness of the commutator generated by the Lipβ（μ） （0 〈β） function and the Marcinkiewicz integral with kernel satisfying certain slightly stronger HSrmander-type condition, respectively,from L^P（μ） to L^q（μ） with 1 〈 p ≤ n/β and 1/q = 1/p - β/n, from the space LP（μ） to Lipβ-n/p（μ） and from the space L^n/β（μ） to RBMO（μ）. Some of the results are also new even for the classical Marcinkiewicz integral.