In this paper, the extremal problem, min, of two convex bodies K and L in ?n is considered. For K to be in extremal position in terms of a decomposition of the identity, give necessary conditions together with the opt...In this paper, the extremal problem, min, of two convex bodies K and L in ?n is considered. For K to be in extremal position in terms of a decomposition of the identity, give necessary conditions together with the optimization theorem of John. Besides, we also consider the weaker optimization problem: min. As an application, we give the geometric distance between the unit ball B2n and a centrally symmetric convex body K.展开更多
In this paper, we consider the extremal problem of the ;p-norm： min{;p（TK）, o E TK C L, T E GL（n）}, where K, L are two convex bodies in Rn. Using the optimization theorem of John, we give necessary conditions for...In this paper, we consider the extremal problem of the ;p-norm： min{;p（TK）, o E TK C L, T E GL（n）}, where K, L are two convex bodies in Rn. Using the optimization theorem of John, we give necessary conditions for K to be in extremal position in terms of a decomposition of the identity. Fhrthermore, the weaker optimization problem, min{（lp（TK））p ： TK C B2n,TK Sn-1 ≠ O,T E GL（n）}, is also considered. As an application, the geometric distance between the unit ball B2n and a centrally symmetric convex body K is obtained.展开更多
Let γ be the Gauss measure on Rn. We establish a Calderon- Zygmund type decomposition and a John-Nirenberg type inequality in terms of the local sharp maximal function and the median value of function over cubes. As ...Let γ be the Gauss measure on Rn. We establish a Calderon- Zygmund type decomposition and a John-Nirenberg type inequality in terms of the local sharp maximal function and the median value of function over cubes. As an application, we obtain an equivalent characterization of known BMO space with Gauss measure.展开更多
文摘In this paper, the extremal problem, min, of two convex bodies K and L in ?n is considered. For K to be in extremal position in terms of a decomposition of the identity, give necessary conditions together with the optimization theorem of John. Besides, we also consider the weaker optimization problem: min. As an application, we give the geometric distance between the unit ball B2n and a centrally symmetric convex body K.
基金Supported by National Natural Science Foundation of China (Grant No. 10971128)Shanghai Leading Academic Discipline Project (Grant No. S30104)Doctoral Fund of Henan Polytechnic University (Grant No. B2011-024)
文摘In this paper, we consider the extremal problem of the ;p-norm： min{;p（TK）, o E TK C L, T E GL（n）}, where K, L are two convex bodies in Rn. Using the optimization theorem of John, we give necessary conditions for K to be in extremal position in terms of a decomposition of the identity. Fhrthermore, the weaker optimization problem, min{（lp（TK））p ： TK C B2n,TK Sn-1 ≠ O,T E GL（n）}, is also considered. As an application, the geometric distance between the unit ball B2n and a centrally symmetric convex body K is obtained.
基金This work was supported by the National Natural Science Foundation of China of China （Grant No. 11571289）.
文摘Let γ be the Gauss measure on Rn. We establish a Calderon- Zygmund type decomposition and a John-Nirenberg type inequality in terms of the local sharp maximal function and the median value of function over cubes. As an application, we obtain an equivalent characterization of known BMO space with Gauss measure.
