Tarnavas established mixed weighted power mean inequality in 1999. A separation of weighted power mean inequslity was derived in this paper. As its applications, some separations of other inequalities were given.
We have pointed out in [1] that so far the L^2 norm inequalities with power weights for the Riesz means σ_R~δ(g)(x) of multiple Fourier integrals have been obtained only by Hirschman and J. L. Rubio de Francia respe...We have pointed out in [1] that so far the L^2 norm inequalities with power weights for the Riesz means σ_R~δ(g)(x) of multiple Fourier integrals have been obtained only by Hirschman and J. L. Rubio de Francia respectively:展开更多
This paper studies the weighted Hardy inequalities on the discrete intervals with four different kinds of boundary conditions. The main result is the uniform expression of the basic estimate of the optimal constant wi...This paper studies the weighted Hardy inequalities on the discrete intervals with four different kinds of boundary conditions. The main result is the uniform expression of the basic estimate of the optimal constant with the corresponding boundary condition. Firstly, one-side boundary condition is considered, which means that the sequences vanish at the right endpoint （ND-case）. Based on the dual method, it can be translated into the case vanishing at left endpoint （DN-case）. Secondly, the condition is the case that the sequences vanish at two endpoints （DD-case）. The third type of condition is the generality of the mean zero condition （NN-case）, which is motivated from probability theory. To deal with the second and the third kinds of inequalities, the splitting technique is presented. Finally, as typical applications, some examples are included.展开更多
By virtue of Cauchy’s integral formula in the theory of complex functions,the authors establish an integral representation for the weighted geometric mean,apply this newly established integral representation to show ...By virtue of Cauchy’s integral formula in the theory of complex functions,the authors establish an integral representation for the weighted geometric mean,apply this newly established integral representation to show that the weighted geometric mean is a complete Bernstein function,and find a new proof of the well-known weighted arithmetic-geometric mean inequality.展开更多
基金Project supported by National Natural Science Foundation of China （Grant No. 10271071）
文摘Tarnavas established mixed weighted power mean inequality in 1999. A separation of weighted power mean inequslity was derived in this paper. As its applications, some separations of other inequalities were given.
文摘We have pointed out in [1] that so far the L^2 norm inequalities with power weights for the Riesz means σ_R~δ(g)(x) of multiple Fourier integrals have been obtained only by Hirschman and J. L. Rubio de Francia respectively:
基金Supported by the Fund for Fostering Talents in Kunming University of Science and Technology(KKZ3202007048)National Natural Science Foundation of China(11801240)。
基金Supported by NSFC(Grant No.11131003)the “985” project from the Ministry of Education in China
文摘This paper studies the weighted Hardy inequalities on the discrete intervals with four different kinds of boundary conditions. The main result is the uniform expression of the basic estimate of the optimal constant with the corresponding boundary condition. Firstly, one-side boundary condition is considered, which means that the sequences vanish at the right endpoint （ND-case）. Based on the dual method, it can be translated into the case vanishing at left endpoint （DN-case）. Secondly, the condition is the case that the sequences vanish at two endpoints （DD-case）. The third type of condition is the generality of the mean zero condition （NN-case）, which is motivated from probability theory. To deal with the second and the third kinds of inequalities, the splitting technique is presented. Finally, as typical applications, some examples are included.
文摘By virtue of Cauchy’s integral formula in the theory of complex functions,the authors establish an integral representation for the weighted geometric mean,apply this newly established integral representation to show that the weighted geometric mean is a complete Bernstein function,and find a new proof of the well-known weighted arithmetic-geometric mean inequality.
