期刊
JOURNAL OF APPROXIMATION THEORY
卷 164, 期 9, 页码 1283-1312出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jat.2012.05.017
关键词
Fourier transforms; Moduli of smoothness; Two-sided estimates; Pitt's inequality
类别
资金
- [MTM 2011-27637]
- [RFFI 10-01-00564]
- [RFFI 12-01-00169]
- [2009 SGR 1303]
- ICREA Funding Source: Custom
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.
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