DIRECT AND INVERSE THEOREMS OF APPROXIMATION THEORY IN BANACH FUNCTION SPACES

作     者：Vinogradov, O. L. 

作者机构：St Petersburg State Univ Universitetskaya nab 7-9 St Petersburg 199034 Russia 

出 版 物：《ST PETERSBURG MATHEMATICAL JOURNAL》 (St. Petersburg Math. J.)

年 卷 期：2024年第35卷第6期

页      面：907-928页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Russian Science Foundation [23-11-00178] 

主　　题：Best approximations moduli of continuity Steklov functions convolution Banach function spaces 

摘      要：. The paper deals with approximation of functions defined on R in spaces that are not translation invariant. The spaces under consideration are Banach function spaces in which Steklov averaging operators are uniformly bounded. It is proved that operators of convolution with a kernel whose bell shaped majorant is integrable are bounded in these spaces. With the help of convolution operators, direct and inverse theorems of the theory of approximation by trigonometric polynomials and entire functions of exponential type are established. As structural characteristics, the powers of deviations of Steklov averages are used, including nonintegral powers. Theorems for periodic and nonperiodic functions are obtained in a unified way. The results of the paper generalize and refine a lot of known theorems on approximation in specific spaces such as weighted spaces, Lebesgue variable exponent spaces and others.