证明Marcinkiewicz积分μΩ与b∈∧β(R^n)生成的Marcinkiewicz积分交换子μΩb是从HKq1^n(1-1/q1)+β,p (R^n)到WKq2^n(1-1/q1)+β,p (R^n)上的有界算子.
Let μΩ be the Marcinkiewicz integral and μΩ, b the commutator generalized by μΩ and b ∈∧β(R^n ). It is proved that μΩ, b is bounded from the Herz-type Hardy space HKq1^n(1-1/q1)+β,p (R^n) into the weak Herz spaceWKq2^n(1-1/q1)+β,p (R^n),where 0〈p≤1,1 〈 q1,q2 〈 ∞ ,1/q2 = 1/q1 - β/n.