齐型空间上奇异积分变换构成的交换子在Morrey空间中的有界性

Boundedness of Commutator of Singular Integral in Morrey Spaces on Homogeneous Spaces

令T为Rn上的Caldero'n- Zygmund积分算子,由T构成的交换子的有界性已有较完善的结论,可将其推广到一般的齐型空间.设(X,d,μ)为齐型空间,利用空间的函数分解方法,可证明由奇异积分变换和BMO(X)中的函数b构成的交换子在齐型Morrey空间和Morrey-Herz空间中的有界性.

Let T be Caldero＇nZygmund operator on Rn ,which is well known that the boundedness of the commutator is related toT and has been widely studied by many experts.In this paper,we prove the boundedness of the commutator is related to the singular integral operator and the function b is in Morrey and MorreyHerz spaces on homogeneous spaces by using the decomposition of the function,where the function b belongs to BMO（X）space.