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Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates
Gorbachev, D.; Tikhonov, Sergey Yu.
Centre de Recerca Matemàtica
We prove two-sided inequalities between the integral moduli of smoothness of a function on R d[superscript] / T d[superscript] 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.
2011
517 - Anàlisi
Transformacions de Fourier
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22 p.
Preprint
Centre de Recerca Matemàtica
Prepublicacions del Centre de Recerca Matemàtica;1092
         

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