本文证明了由参数型Marcinkiewicz积分Mρ和Lipshitz函数b生成的交换子Mρ的有界性.在M的核函数满足较强的HOrmander条件下,证明了MPq不仅从Morrey空间MPq(μ)到RBMO(μ)有界,从Lebesgue空间Ln/β(μ)到空间RBM0(μ)有界,而且从Morrey空间MPq(μ)到Lipschitz空间Lip(β-n/p)(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