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

By Dmitry V. Gorbachev, S. Tikhonov. 2012

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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.

Subfields: Applied Mathematics, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d8d5a097af75b1d69b38b76086302d58a6d17a9e