带权Lorentz空间上Hardy算子的对偶算子

The dual operator of the Hardy operator on Lorentz spaces with weights

设(x≥0)为Hardy算子的对偶算子,0<p,q,r,s≤∞.本文得到算子Q从Lorentz空间L^(r,s)((0,∞),vdx)到L^(p,q)((0,∞),wdx)有界的权函数对(w(x),v(x))的特征。

Let Qf(x) = fx+∞f(t)dt(x≥0) be the dual operator of the Hardy operator, 0< p,q,s≤∞. Characterizations are obtained for those pairs of weight functions w(x),v(x) fo the operator Q is bounded from the Lorentz space .