超奇异的Marcinkiewicz积分交换子的有界性

Boundedness of Commutators Related to Hyper-singular Marcinkiewicz Integral Commutator

研究了由一类超奇异的Marcinkiewicz积分和Lipβ(Rn)(0<β≤1)函数生成的交换子μbΩ,ρ.证明了当可变核Ω(x,z)∈L∞(Rn)×Lr(Sn-1)(r>2(n-1)/n)时,交换子μbΩ,ρ在齐次Morrey-Herz空间M K.αp,,qλ(Rn)上的有界性,同时建立了参数型Marcinkiewicz积分交换子μbΩ,,σρ在齐次Morrey-Herz空间上的有界性,拓宽了以往的结果.

We study the boundedness of hyper-singular Marcinkiewicz integral μΩ.ρ^bgenerated by function Lipβ（R^n）（0〈β≤1） and a certain Marcinkiewicz integrals with variable kernel Ω（x,z）∈L^∞（R^n）×L^r（S^n-1）（r〉2（n-1）/n） in the homogeneous Morrey-Herz spaces. Moreover, the same results are shown for the commutator μΩ.ρ^b,σ related to the parametric Marcinkiewicz integral.