带变量核的 Marcinkiewicz 积分交换子的加权Campanato估计

Weighted Campanato Estimates for Commutators of Marcinkiewicz Integrals with Variable Kernel

摘要: 将交换子中的函数 b由加权 Lipschitz空间推广到加权 Campanato空间,使用 Sharp极大函数,证明了带变量核的 Marcinkiewicz积分算子μΩ和某一类加权 Campanato空间的函数 b生成的交换子μbΩ是由 Lp(ω)到Lq(ω1-q) 的有界算子,从而使用范围更广.

Abstract: Functionbin commutator is extended from the weighted Lipschitz space to the weighted Campanato space. By use of the sharp maximal function, it is proved that the Marcinkiewicz integral operatorμΩwith viariable kernel and the commu- tatorμbΩgenerated by a weighted Campanato space functionb, are a bounded operator fromLp(ω) to Lq(ω1-q) by use of Sharp maximal function. Thus,the range of use is made still wider.