Bernstein inequality played an important role in approximation theory and Fourier analysis. This article first introduces a general system of functions and the socalled multivariate weighted Bernstein, Nikol＇skii, an...Bernstein inequality played an important role in approximation theory and Fourier analysis. This article first introduces a general system of functions and the socalled multivariate weighted Bernstein, Nikol＇skii, and Ul＇yanov-type inequalities. Then, the relations among these three inequalities are discussed. Namely, it is proved that a family of functions equipped with Bernstein-type inequality satisfies Nikol＇skii-type and Ul＇yanov-type inequality. Finally, as applications, some classical inequalities are deduced from the obtained results.展开更多
In the present paper we extend previous results about the monotoaicity of Bernstein-type operators rdtiwe to convex functions and about the preservation of Lipschitz classes.
We establish Jackson-type and Bernstein-type inequalities for multipliers on Herz-type Hardy spaces. These inequalities can be applied to some important operators in Fourier analysis, such as the Bochner-Riesz multipl...We establish Jackson-type and Bernstein-type inequalities for multipliers on Herz-type Hardy spaces. These inequalities can be applied to some important operators in Fourier analysis, such as the Bochner-Riesz multiplier over the critical index, the generalized Bochner-Riesz mean and the generalized Able-Poisson operator.展开更多
We derive the Hessian estimate of the w-function defined on the pseudo-Grassmann manifold Gnmm, which is convex by the estimate. As an application, we give a direct proof of the Bernstein-type theorem due to Y. Xin [M...We derive the Hessian estimate of the w-function defined on the pseudo-Grassmann manifold Gnmm, which is convex by the estimate. As an application, we give a direct proof of the Bernstein-type theorem due to Y. Xin [Mannscripta Math., 2000, 103： 191-202]. We also estimate the squared norm of the second fundamental form of a complete spacelike submanifold in pseudoEuclidean space in terms of the w-function and the mean curvature.展开更多
针对多小区下行多进单出(multiple-input single-output,MISO)干扰信道,在控制每个用户信漏噪比(signal to leakage plus noise ratio,SLNR)低于门限值的概率小于中断概率的约束条件下,以最小化系统总加权发射功率为优化目标设计线性预...针对多小区下行多进单出(multiple-input single-output,MISO)干扰信道,在控制每个用户信漏噪比(signal to leakage plus noise ratio,SLNR)低于门限值的概率小于中断概率的约束条件下,以最小化系统总加权发射功率为优化目标设计线性预编码。利用半定松弛和Bernstein-type不等式,将非凸的具有随机性的原始优化问题转换为确定性凸优化问题。仿真结果表明,所提出的预编码设计比worst-case等比较方案耗费的总加权发射功率更少。展开更多
基金supported by the National Natural Science Foundation of China (90818020,60873206)the Foundation of Innovation Team of Science and Technology of Zhejiang Province of China (2009R50024)
文摘Bernstein inequality played an important role in approximation theory and Fourier analysis. This article first introduces a general system of functions and the socalled multivariate weighted Bernstein, Nikol＇skii, and Ul＇yanov-type inequalities. Then, the relations among these three inequalities are discussed. Namely, it is proved that a family of functions equipped with Bernstein-type inequality satisfies Nikol＇skii-type and Ul＇yanov-type inequality. Finally, as applications, some classical inequalities are deduced from the obtained results.
文摘In the present paper we extend previous results about the monotoaicity of Bernstein-type operators rdtiwe to convex functions and about the preservation of Lipschitz classes.
基金supported by Key Academic Discipline of Zhejiang Province of China and National NaturalScience Foundation of China (Grant Nos. 10571014, 10631080, 10671019)
文摘We establish Jackson-type and Bernstein-type inequalities for multipliers on Herz-type Hardy spaces. These inequalities can be applied to some important operators in Fourier analysis, such as the Bochner-Riesz multiplier over the critical index, the generalized Bochner-Riesz mean and the generalized Able-Poisson operator.
文摘We derive the Hessian estimate of the w-function defined on the pseudo-Grassmann manifold Gnmm, which is convex by the estimate. As an application, we give a direct proof of the Bernstein-type theorem due to Y. Xin [Mannscripta Math., 2000, 103： 191-202]. We also estimate the squared norm of the second fundamental form of a complete spacelike submanifold in pseudoEuclidean space in terms of the w-function and the mean curvature.
文摘针对多小区下行多进单出(multiple-input single-output,MISO)干扰信道,在控制每个用户信漏噪比(signal to leakage plus noise ratio,SLNR)低于门限值的概率小于中断概率的约束条件下,以最小化系统总加权发射功率为优化目标设计线性预编码。利用半定松弛和Bernstein-type不等式,将非凸的具有随机性的原始优化问题转换为确定性凸优化问题。仿真结果表明,所提出的预编码设计比worst-case等比较方案耗费的总加权发射功率更少。
