Moduli of smoothness and growth properties of Fourier transforms: Two-sided estimates

JOURNAL OF APPROXIMATION THEORY

卷:164

Article

Gorbachev, Dmitry³  Tikhonov, Sergey^1,2 

[1] ICREA, Bellaterra 08193, Barcelona, Spain

[2] Ctr Recerca Matemat, Bellaterra 08193, Barcelona, Spain

[3] Tula State Univ, Dept Mech & Math, Tula 300600, Russia

关键词: Fourier transforms;    Moduli of smoothness;    Two-sided estimates;    Pitt's inequality;   

DOI  :  10.1016/j.jat.2012.05.017

来源: Elsevier

【 摘 要 】

We prove two-sided inequalities between the integral moduli of smoothness of a function on R-d/T-d and the weighted tail-type integrals of its Fourier transform/series. Sharpness of obtained results in particular is given by the equivalence results for functions satisfying certain regular conditions. Applications include a quantitative form of the Riemann-Lebesgue lemma as well as several other questions in approximation theory and the theory of function spaces. (c) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free