一类向量值的加权模不等式

A Class of Vector-Valued Weighted Norm Inequalities

摘要: 对于向量值函数空间LpB(Rn,ωdx)中的极大算子,利用Ho..lder不等式及广义Minkowski不等式,对给定的权函数v(x)≥0存在另一个权函数ω(x)<∞,a.ex∈Rn,使得Hardy-Littlewood极大算子从LpB(Rn,ωdx)到Lp(Rn,vdx)是有界的.

Abstract: Using H（o··）lder inequality and extended Minkowski inequality, a sufficient condition on the weight function v （x）≥0 is obtained such that the Hardy-Littlewood maximal operator is bounded from L^p_B （Rn, ω dx） to L^p （Rn , v dx） for some ω （x）<∞, a.e x∈Rn .