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

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

2012-04-19

arxiv.org/abs/1204.4392v2

Mathematics

Classical Analysis and ODEs

22 pages

Scientific paper

We prove two-sided inequalities between the integral moduli of smoothness of a function on $\mathbb{R}^d/\mathbb{T}^d$ 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.

Affiliated with

Also associated with

No associations

Rating

Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-35296