一致度量下Jackson-Stechkin不等式中的正合常数

度量光滑性的函数与Jackson-Stechkin定理中的常数

Functions measuring smoothness and the constants in Jackson--Stechkin theorem

本文讨论了逼近论中两类正定理的等价性：a）关于光滑函数的正定理（Favard估计）。b）对于任意连续函数（Jackson-Stechkin估计）。具体地说，我们将证明杰克逊-Stechkin不等式与最佳的光滑常数的顺序如下Favard不等式。

Jackson-Stechkin定理中关于差与常数的Bohr-Favard不等式

Bohr--Favard Inequality for differences and constants in Jackson--Stechkin Theorem

我们考虑三角多项式的一致逼近。本文的目的是获得Jackson-Stechkin常数$J_m$的良好估计。我们证明了$ J_m \le C 2^{-m+5/2\log_2m}$ .我们的证明是基于Bohr-Favard不等式的差分模拟。

Jackson-Stechkin type inequalities for differentiable functions in weighted Orlicz spaces

In the present work some Jackson Stechkin type direct theorems of trigonometric approximation are proved in Orlicz spaces with weights satisfying some Muckenhoupt's $A_{p}$ condition. To obtain refined version of the Jackson type inequality we prove an extrapolation theorem, Marcinkiewicz multiplier theorem and Littlewood Paley type results. As a consequence refined inverse Marchaud type inequalities are obtained. By means of a realization result we find an equivalence between the fractional order weighted modulus of smoothness and the classical weighted Peetre's K-functional.

A note on $K$-functional, Modulus of smoothness, Jackson theorem and Nikolskii-Stechkin inequality on Damek-Ricci spaces

In this paper we study approximation theorems for $L^2$-space on Damek-Ricci spaces. We prove direct Jackson theorem of approximations for the modulus of smoothness defined using spherical mean operator on Damek-Ricci spaces. We also prove Nikolskii-Stechkin inequality. To prove these inequalities we use functions of bounded spectrum as a tool of approximation. Finally, as an application, we prove equivalence of the $K$-functional and modulus of smoothness for Damek-Ricci spaces.

关于$T_{2n-1}^\perp$空间

On $T_{2n-1}^\perp$ spaces

本文主要讨论由$T_{2n-1}^\perp$导出的函数均值不等式。经典Jackson不等式在第二连续模情形下的简单证明可以看作是我们估计的结果。讨论了经典Stechkin不等式中的锐常数问题。

On the optimal constants in the two-sided Stechkin inequalities

We address the optimal constants in the strong and the weak Stechkin inequalities, both in their discrete and continuous variants. These inequalities appear in the characterization of approximation spaces which arise from sparse approximation or have applications to interpolation theory. An elementary proof of a constant in the strong discrete Stechkin inequality given by Bennett is provided, and we improve the constants given by Levin and Stechkin and by Copson. Finally, the minimal constants in the weak discrete Stechkin inequalities and both continuous Stechkin inequalities are presented.