The boundedness of the commutator μΩ,b generalized by Marcinkiewicz integral μΩ and a function b(x) ∈ CBMOq(Rn) on homogeneous Morrey-Herz spaces is established.
We study certain square functions on product spaces Rn × Rm, whose integral kernels are obtained from kernels which are homogeneous in each factor Rn and Rm and locally in L(log+ L) away from Rn × {0} and {0} × Rm by means of polynomial distortions in the radial variable. As a model case, we obtain that the Marcinkiewicz integral operator is bounded on Lp(Rn × Rm)(p＞1) for Ω ∈ Llog+ L(Sn-1 × Sm-1) satisfying the cancellation condition.
WANG Meng, CHEN Jiecheng2 & FAN Dashan Department of Mathematics, Zhejiang University (at Yuquan campus), Hangzhou 310027, China
