变量核奇异积分算子交换子的紧性

Compactness of Commutators of Singular Integral Operations with Variable Kernel

证明了在一定条件下,带变量核的奇异积分算子交换子[b,T]是L^p上的紧算子,也证明了,如核函数满足一定的条件,并且带变量核的奇异积分算子的交换子[b,T]是L^p上的有界算子或紧算子,那么b∈BMO(R^n)或b∈CMO(R^n).

This paper proves that, under certain conditions, the commutator [b, T] of the singular integral operator with variable kernel is a compact operator on L^p. Moreover, the authors show also that if the kernel satisfies some conditions, and the commutator [b, T] of the singular integral operator with variable kernel is a bounded or compact operator on L^p, then b∈ BMO or b ∈ CMO, respectively.