本文证明了:当核函数Ω是零次齐次的,且满足某种对数型Lipschitz条件时,Marcinkiewicz积分μΩ的交换子是从局部Hardy空间h~1(R~n)到空间h_q~1(R~n)= h~1(R~n)+L~q(R~n)(q>1)上的有界算子。

We show that the commutator of Marcinkiewicz integralμΩis bounded from local Hardy spaces h~1(R~n) into spaces h_q~1(R~n) = h~1(R~n) + L~q(R~n)(q>1).Here the kernel is a homogeneous function of degree zero with cancellation property and satisfies the logarithmic type Lipschitz conditions.