设ωi(x,r)(i=1,2)是R^n×R+上的可测正函数,当(ω1,ω2)∈S0,n时,由BMO函数与极大算子M生成的交换子,是从广义Morrey空间Lp,ω1(Rn)到Lp,ω2(Rn)的有界算子.对于奇异积分算子T以及Riesz积分位势算子如生成的交换子,也得到了相似的有界性结果.该结论推广了Mizuhara在广义Morrey空间上的相关结论.
Let wi(x, r) (i = 1, 2) be a positive measurable function in Rn x R+. If (wl, w2) C S0,n, then the commutators generated by the BMO function and maximal operators M are bounded from Lp,ω1 (Rn) to Lp,ω2 (Rn). Similarly, the commutators generated by the singular integral operator T and the Riesz potential operator Is are also bounded on generalized Morrey spaces. All the results generalize the corresponding results of Mizuhara on the generalized Morrey spaces.