具有非倍测度的参数型Marcinkiewicz积分交换子估计

Estimates for Commutators of Parameter Marcinkiewicz Integrals with Non-Doubling Measures

本文证明了由参数型Marcinkiewicz积分Mρ和Lipshitz函数b生成的交换子Mρb的有界性.在M的核函数满足较强的Hrmander条件下,证明了Mρb不仅从Morrey空间Mpq(μ)到RBMO(μ)有界,从Lebesgue空间Ln/β(μ)到空间RBMO(μ)有界,而且从Morrey空间Mpq(μ)到Lipschitz空间Lip(β-np)(μ)有界,这里p=n/β.

In this paper, the authors prove the boundedness of the commutator MPq generated by the parameter Marcinkiewicz integral Me with Lipschitz function b. With the assumption that the kernel of M satisfies certain slightly stronger H0rmander-type condition, the authors prove that MPq is hounded from the Morrey space MPq（μ） to the space RBMO ~）, from the space Ln/P（μ） to the space RBMO（μ）, and from the Morrey space MPq（μ） to the Lipschitz space Lip（β-n/p） （μ） , here p =n/β