非倍测度条件下Marcinkiewicz积分及其交换子在Morrey空间中的有界性

The boundedness of Marcinkiewicz integral commutators on morrey spaces with non doubling measures

讨论了测度μ在满足非倍条件下,Marcinkiewicz积分算子及其与RBMO(μ)函数、Lipschitz函数生成的交换子的有界性,通过Marcinkiewica积分及该交换子在Lebesgue空间中的有界性,得到了该算子及交换子在非齐型空间上的Morrey空间中的有界性.

In this paper, the authors discusses the boundedness of a class of Marcinkiewicz integral and commutators generated by the Marcinkiewicz integral with RBMO（μ） functions or Lipschitz functions , under the assumption that μ is a non-doubling measure on r^d. By means of the boudedness of Marcinkiewicz integral and the commutaters on Lebesgue space, the authors obtain the boundedness of Marcinkiewicz integral and the commutaters on Morrey space with non-doubling measures.