Let p（z） be a polynomial of degree at most n. In this paper we obtain some new results about the dependence of on [[P（Z）[ls for every α, β∈ C with ｜a｜≤ 1, ｜β｜〉 1, R 〉 r 〉 1, and s 〉 O. Our results not...Let p（z） be a polynomial of degree at most n. In this paper we obtain some new results about the dependence of on [[P（Z）[ls for every α, β∈ C with ｜a｜≤ 1, ｜β｜〉 1, R 〉 r 〉 1, and s 〉 O. Our results not only generalize some well known inequalities, but also are variety of interesting results deduced from them by a fairly uniform procedure.展开更多
In this paper, we study the constants in a version of Rosenthal’s inequality for locally square integrable martingales. We prove that the order of growth rates of the constants is the same as in the case of discrete ...In this paper, we study the constants in a version of Rosenthal’s inequality for locally square integrable martingales. We prove that the order of growth rates of the constants is the same as in the case of discrete time martingales.展开更多
Lp Poincare inequalities for general symmetric forms are established by new Cheeger＇s isoperimetric constants. Lp super-Poincare inequalities are introduced to describe the equivalent conditions for the Lp compact em...Lp Poincare inequalities for general symmetric forms are established by new Cheeger＇s isoperimetric constants. Lp super-Poincare inequalities are introduced to describe the equivalent conditions for the Lp compact embedding, and the criteria via the new Cheeger＇s constants for those inequalities are presented. Finally, the concentration or the volume growth of measures for these inequalities are studied.展开更多
Weak log-Sobolev and Lp weak Poincare inequalities for general symmetric forms are investigated by using newly defined Cheeger＇s isoperimetric constants. Some concrete examples of ergodic birth-death processes are al...Weak log-Sobolev and Lp weak Poincare inequalities for general symmetric forms are investigated by using newly defined Cheeger＇s isoperimetric constants. Some concrete examples of ergodic birth-death processes are also presented to illustrate the results.展开更多
The mixed principal eigenvalue of p-Laplacian （equivalently, the optimal constant of weighted Hardy inequality in Lp space） is studied in this paper. Several variational formulas for the eigenvalue are presented. As...The mixed principal eigenvalue of p-Laplacian （equivalently, the optimal constant of weighted Hardy inequality in Lp space） is studied in this paper. Several variational formulas for the eigenvalue are presented. As applications of the formulas, a criterion for the positivity of the eigenvalue is obtained. Furthermore, an approximating procedure and some explicit estimates are presented case by case. An example is included to illustrate the power of the results of the paper.展开更多
文摘Let p（z） be a polynomial of degree at most n. In this paper we obtain some new results about the dependence of on [[P（Z）[ls for every α, β∈ C with ｜a｜≤ 1, ｜β｜〉 1, R 〉 r 〉 1, and s 〉 O. Our results not only generalize some well known inequalities, but also are variety of interesting results deduced from them by a fairly uniform procedure.
基金the National Natural Science Foundation of China (No.10571176)
文摘In this paper, we study the constants in a version of Rosenthal’s inequality for locally square integrable martingales. We prove that the order of growth rates of the constants is the same as in the case of discrete time martingales.
基金Supported in part by Program for New Century Excellent Talents in University (NCET)973 Project (Grant No.2006CB805901)National Natural Science Foundation of China (Grant No.10721091)
文摘Lp Poincare inequalities for general symmetric forms are established by new Cheeger＇s isoperimetric constants. Lp super-Poincare inequalities are introduced to describe the equivalent conditions for the Lp compact embedding, and the criteria via the new Cheeger＇s constants for those inequalities are presented. Finally, the concentration or the volume growth of measures for these inequalities are studied.
文摘Weak log-Sobolev and Lp weak Poincare inequalities for general symmetric forms are investigated by using newly defined Cheeger＇s isoperimetric constants. Some concrete examples of ergodic birth-death processes are also presented to illustrate the results.
基金Acknowledgements The authors would like to thank Professor Yonghua Mao for his helpful comments and suggestions. This work was supported in part by the National Natural Science Foundation of China （Grant No. 11131003）, the Specialized Research Fund for the Doctoral Program of Higher Education （Grant No. 20100003110005）, the ＇985＇ project from the Ministry of Education in China, and the Fundamental Research Funds for the Central Universities.
文摘The mixed principal eigenvalue of p-Laplacian （equivalently, the optimal constant of weighted Hardy inequality in Lp space） is studied in this paper. Several variational formulas for the eigenvalue are presented. As applications of the formulas, a criterion for the positivity of the eigenvalue is obtained. Furthermore, an approximating procedure and some explicit estimates are presented case by case. An example is included to illustrate the power of the results of the paper.
