We prove the L estimate for the isotropic version of the homogeneous landau problem, which was explored by M. Gualdani and N. Guillen. As shown in a region of the smooth potentials range under values of the interactio...We prove the L estimate for the isotropic version of the homogeneous landau problem, which was explored by M. Gualdani and N. Guillen. As shown in a region of the smooth potentials range under values of the interaction exponent (2), a weighted Poincaré inequality is a natural consequence of the traditional weighted Hardy inequality, which in turn implies that the norms of solutions propagate in the L1 space. Now, the L estimate is based on the work of De Giorgi, Nash, and Moser, as well as a few weighted Sobolev inequalities.展开更多
Let F_n be the Kaplan-Meier estimator of distribution function F. Let J(·) be a measureable real-valued function. In this paper, a U-statistic representation for the Kaplan-Meier L-estimator, T(F_n)=∫xJ( _n(x))d...Let F_n be the Kaplan-Meier estimator of distribution function F. Let J(·) be a measureable real-valued function. In this paper, a U-statistic representation for the Kaplan-Meier L-estimator, T(F_n)=∫xJ( _n(x))d _n(x), is derived. Furthermore the representation is also used to establish a Berry-Essen inequality for T( _n).展开更多
文摘We prove the L estimate for the isotropic version of the homogeneous landau problem, which was explored by M. Gualdani and N. Guillen. As shown in a region of the smooth potentials range under values of the interaction exponent (2), a weighted Poincaré inequality is a natural consequence of the traditional weighted Hardy inequality, which in turn implies that the norms of solutions propagate in the L1 space. Now, the L estimate is based on the work of De Giorgi, Nash, and Moser, as well as a few weighted Sobolev inequalities.
基金Research supported by the National Natural Science Foundation of Chinaa CRCG grant of the University of Hong Kong
文摘Let F_n be the Kaplan-Meier estimator of distribution function F. Let J(·) be a measureable real-valued function. In this paper, a U-statistic representation for the Kaplan-Meier L-estimator, T(F_n)=∫xJ( _n(x))d _n(x), is derived. Furthermore the representation is also used to establish a Berry-Essen inequality for T( _n).
