一类变量核奇异积分交换子在Morrey空间中的紧性

Compactness of a Class of Singular Integral Commutators with Variable Kernels in Morrey Spaces

利用球调和函数证明一类变量核奇异积分交换子[b,T]是Morrey空间L^(p,α)(R^n)(1<p<∞,0<α<n)上的紧算子.结果表明,在一定条件下,若存在p(1<p<∞),使得当交换子[b,T]是Morrey空间L^(p,α)(R^n)上的紧算子时,则b∈VMO(R^n).

Using spherical harmonic functions,we proved that a class of singular integral commutators with variable kernels [b,T]was compact operator on Morrey spaces L^（p,α）（R^n）for 1p ∞ and0αn.The results show that,under a certain condition,we obtain b∈ VMO（R^n）if the commutator[b,T]is compact operator on Morrey space L^（p,α）（R^n）for some 1p∞.