A sufficient condition on the existence of a global weak sharp minima for general function in metric space is established. A characterization for convex function to have global weak sharp minima is also presented, whi...A sufficient condition on the existence of a global weak sharp minima for general function in metric space is established. A characterization for convex function to have global weak sharp minima is also presented, which generalized Burke and Ferris' result to infinite dimensional space. A characterization of the completeness of a metric space is given by the existence of global weak sharp minima.展开更多
We obtain the operator norms of the n-dimensional fractional Hardy operator Hα(0 〈 α 〈 n) from weighted Lebesgue spaces Lp|x|p(R^n) to weighted weak Lebesgue spacesLq,∞|x|β(R^n).
基金The research was supported by the National Natural Science Foundation of China(10361008) Natural Science Foundation of Yunnan Province(2003A002M)
文摘A sufficient condition on the existence of a global weak sharp minima for general function in metric space is established. A characterization for convex function to have global weak sharp minima is also presented, which generalized Burke and Ferris' result to infinite dimensional space. A characterization of the completeness of a metric space is given by the existence of global weak sharp minima.