关于Vitali族的分数次极大算子的加权不等式

The Weighted Inegualities for Fractional Maximal Operators with respect to Vitali Families

设B={B_α} α>0是R^n中的Vitali族,0≤γ<1,定义γ阶分数次极大算子如下:本文得到了上述分数次极大算子的加权弱型不等式和加权强型不等式。

Let B = {Ba} a&gt;0 be the Vitali family in Rn, 0&lt;?&lt;1 we definite the following maximal operator with respect to B.Mγf(x,t)=supl/1-γ ∫│f(y)│dy │(?)│&gt;1n │Ba│1-γ x+BcIn this paper, we get the weighed weak type inequality and the weigthed strang type inequality for that fractional maximal operator.