Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Cesàro Means of Trigonometric Fourier Series

Cesàro Means of Trigonometric Fourier Series L. Zhizhiashvili proved that if for some 𝑝, 1 ≤ 𝑝 ≤ ∞, and α ∈ (0, 1), then the 𝐿 𝑝 -deviation of 𝑓 from its Cesàro mean is 𝑂(𝑛 α 𝑤(1/𝑛)) where 𝑤(·) is a modulus of continuity. In this paper we show that this estimation is non-amplifiable for 𝑝 = 1. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

Cesàro Means of Trigonometric Fourier Series

Goginava, U.
Georgian Mathematical Journal , Volume 9 (1) – Mar 1, 2002
Download PDF
4 pages

Loading next page...
 
/lp/de-gruyter/ces-ro-means-of-trigonometric-fourier-series-Y4OOqhB4Dy

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.2002.53
Publisher site
See Article on Publisher Site

Abstract

L. Zhizhiashvili proved that if for some 𝑝, 1 ≤ 𝑝 ≤ ∞, and α ∈ (0, 1), then the 𝐿 𝑝 -deviation of 𝑓 from its Cesàro mean is 𝑂(𝑛 α 𝑤(1/𝑛)) where 𝑤(·) is a modulus of continuity. In this paper we show that this estimation is non-amplifiable for 𝑝 = 1.

Journal

Georgian Mathematical Journal – de Gruyter

Published: Mar 1, 2002

Keywords: Trigonometric Fourier series; Cesàro means

There are no references for this article.