RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Izv. RAN. Ser. Mat.: Year: Volume: Issue: Page: Find

 Izv. Akad. Nauk SSSR Ser. Mat., 1973, Volume 37, Issue 2, Pages 399–421 (Mi izv2254)

The asymptotic $L_p$-norm of differentiated Fourier sums of functions of bounded variation

B. I. Golubov

Abstract: An asymptotic expression as $n\to\infty$ is found for the norms $\|S_n^{(r)}(x,f)\|_{L_q}$ ($1\le p<q<\infty$, $r=1,2,…$), where $S_n(x,f)$ is a Fourier sum of the $2\pi$-periodic function $f(x)$ having bounded $p$-variation. Various criteria for the continuity of a function of bounded $p$-variation are obtained as corollaries.

Full text: PDF file (1740 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1973, 7:2, 401–423

Bibliographic databases:

UDC: 517.5
MSC: Primary 42A16, 26A45; Secondary 26A15

Citation: B. I. Golubov, “The asymptotic $L_p$-norm of differentiated Fourier sums of functions of bounded variation”, Izv. Akad. Nauk SSSR Ser. Mat., 37:2 (1973), 399–421; Math. USSR-Izv., 7:2 (1973), 401–423

Citation in format AMSBIB
\Bibitem{Gol73} \by B.~I.~Golubov \paper The asymptotic $L_p$-norm of differentiated Fourier sums of functions of bounded variation \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1973 \vol 37 \issue 2 \pages 399--421 \mathnet{http://mi.mathnet.ru/izv2254} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=364989} \zmath{https://zbmath.org/?q=an:0264.42003} \transl \jour Math. USSR-Izv. \yr 1973 \vol 7 \issue 2 \pages 401--423 \crossref{https://doi.org/10.1070/IM1973v007n02ABEH001945} 

• http://mi.mathnet.ru/eng/izv2254
• http://mi.mathnet.ru/eng/izv/v37/i2/p399

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. M. S. Bespalov, “Explicit form of the Dirichlet kernel for Walsh series and transformations”, Sb. Math., 196:7 (2005), 935–957
•  Number of views: This page: 216 Full text: 71 References: 28 First page: 1