一类奇异积分算子的交换子的有界性

研究积分算子在函数空间中的有界性一直是分析数学的中心问题之一，交换子就是其中一类重要的算子，其重要性在于交换子可以被用来刻划某些函数空间，所以研究与各种积分算子相关的交换子很自然地就显得比较重要而有意义．本文先给出了一类满足变H6rmander条件的奇异积分算子所构成的交换子，然后证明了该交换子的sharp极大函数估计．最后，我们研究了该交换子在Lebesgue空间、Morrey空间以及Triebel-Lizorkin空间上的有界性问题．

Boundedness of Commutator Related to Certain Singular Integral Operator

It is main one of problems in analysis mathematics to study the boundedness of integral operator on function spaces, commutator can serve as a tool to describe some function spaces. As a consequence, it is natural and significant to study commutators concerned with miscellaneous integral operators. On the other hand, singular integral operator is a kind of classic and important operator in the field of harmonic analysis. This paper is mainly to introduce the commutator related to a kind of singular integral operator,and to investigate its boundedness. At the beginning of this paper,both the definition of commutators related to singular integral operators satisfying a variant of H~irmander＇ s condition is given. And we prove the sharp maximal function inequities of the commutator. Afterwards, we obtain the boundedness of the commutator on Lebesgue, Morrey and Triebel-Lizorkin spaces.