粗糙核分数次积分交换子在齐次Morrey-Herz空间上的CBMO估计

CBMO Estimates for Commutators of Rough Fractional Integrals on Homogeneous Morrey-Herz Spaces

带粗糙核的分数次积分交换子定义为[b,TΩ,l]f(x)=∫RnΩ(x-y)|x-y|n-l(b(x)-b(y))f(y)dy,其中Ω∈Ls(Sn-1),1≤s<∞,是零次齐次函数,b∈CBMOq(Rn).在一定条件下,得到了分数次积分交换子[b,TΩ,l]及其相应的极大算子在齐次Morrey-Herz空间上的CBMO估计.

The commutators of the fractional integrals with rough kernel is defined by [b,TΩ,l]f（′x）=∫R^nΩ（x-y）/｜x-y｜^n-l（b（x）-b（y））f（y）dy,Ω∈L^s（S^n-1）,1≤s〈∞,where Ω∈L^s （ S^n-1 ）, 1 ≤ s 〈 ∞, is a homogeneous of degree zero, b ∈ CBMOq （ R^n）. Under a certain condition, the CBMO estimates for the commutators of the fractional integrals with rough kernel [ b, TΩ, l ] and its maximal operator on the homogeneous Morrey-Herz spaces are obtained.