In this paper, weighted estimates with general weights are established for the multilinear singular integral operator defined by TAf（x）=p.v.∫R^n Ω（x-y）/｜x-y）^n＋1（A（x）-A（y）-△↓A（y）（x-y）f（y）dywhere ...In this paper, weighted estimates with general weights are established for the multilinear singular integral operator defined by TAf（x）=p.v.∫R^n Ω（x-y）/｜x-y）^n＋1（A（x）-A（y）-△↓A（y）（x-y）f（y）dywhere fl is homogeneous of degree zero, has vanishing moment of order one, and belongs to Lipγ（S^n-1） with γ∈ （0, 1], A has derivatives of order one in BMO（R^n）.展开更多
Some maximal moment inequalities for partial sums of the strong mixing random variable sequence are established. These inequalities use moment sums as up-boundary and improve the corre- sponding ones obtained by Shao ...Some maximal moment inequalities for partial sums of the strong mixing random variable sequence are established. These inequalities use moment sums as up-boundary and improve the corre- sponding ones obtained by Shao （1996）. To show the application of the inequalities, we apply them to discuss the asymptotic normality of the weight function estimate for the fixed design regression model.展开更多
文摘In this paper, weighted estimates with general weights are established for the multilinear singular integral operator defined by TAf（x）=p.v.∫R^n Ω（x-y）/｜x-y）^n＋1（A（x）-A（y）-△↓A（y）（x-y）f（y）dywhere fl is homogeneous of degree zero, has vanishing moment of order one, and belongs to Lipγ（S^n-1） with γ∈ （0, 1], A has derivatives of order one in BMO（R^n）.
基金the Natural Science Foundation of China(10161004)the Natural Science Foundation of Guangxi(04047033)
文摘Some maximal moment inequalities for partial sums of the strong mixing random variable sequence are established. These inequalities use moment sums as up-boundary and improve the corre- sponding ones obtained by Shao （1996）. To show the application of the inequalities, we apply them to discuss the asymptotic normality of the weight function estimate for the fixed design regression model.
