Trudy Instituta Matematiki i Mekhaniki UrO RAN
 RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Trudy Inst. Mat. i Mekh. UrO RAN: Year: Volume: Issue: Page: Find

 Personal entry: Login: Password: Save password Enter Forgotten password? Register

 Trudy Inst. Mat. i Mekh. UrO RAN, 2005, Volume 11, Number 2, Pages 10–29 (Mi timm186)

This article is cited in 4 scientific papers (total in 4 papers)

Growth rate of sequences of multiple rectangular Fourier sums

N. Yu. Antonov

Abstract: In the case when a sequence of $d$-dimensional vectors $\mathbf n_k=(n_k^1,n_k^2,…,n_k^d)$ with nonnegative integral coordinates satisfies the condition
$$n_k^j=\alpha_jm_k+O(1),\quad k\in\mathbb N,\quad1\le j\le d,$$
where $\alpha_1…,\alpha_d$ are nonnegative real numbers and $\{m_k\}_{k=1}^\infty$ is a sequence of positive integers, the following estimate of the rate of growth of sequences $S_{\mathbf n_k}(f,\mathbf x)$ of rectangular partial sums of multiple trigonometric Fourier series is obtained: if $f\in L(\ln^+L)^{d-1}([-\pi,\pi)^d)$, then
$$S_{\mathbf n_k}(f,\mathbf x)=o(\ln k)\quada.e.$$
Analogous estimates are valid for conjugate series as well.

Full text: PDF file (359 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2005, suppl. 2, S9–S29

Bibliographic databases:
UDC: 517.518
Received: 16.01.2005

Citation: N. Yu. Antonov, “Growth rate of sequences of multiple rectangular Fourier sums”, Function theory, Trudy Inst. Mat. i Mekh. UrO RAN, 11, no. 2, 2005, 10–29; Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 2, S9–S29

Citation in format AMSBIB
\Bibitem{Ant05} \by N.~Yu.~Antonov \paper Growth rate of sequences of multiple rectangular Fourier sums \inbook Function theory \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2005 \vol 11 \issue 2 \pages 10--29 \mathnet{http://mi.mathnet.ru/timm186} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2200219} \zmath{https://zbmath.org/?q=an:1143.42010} \elib{https://elibrary.ru/item.asp?id=12040700} \transl \jour Proc. Steklov Inst. Math. (Suppl.) \yr 2005 \issue , suppl. 2 \pages S9--S29 

Linking options:
• http://mi.mathnet.ru/eng/timm186
• http://mi.mathnet.ru/eng/timm/v11/i2/p10

 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. N. Yu. Antonov, “On the almost everywhere convergence of sequences of multiple rectangular Fourier sums”, Proc. Steklov Inst. Math. (Suppl.), 264, suppl. 1 (2009), S1–S18
2. N. Yu. Antonov, “On the growth rate of arbitrary sequences of double rectangular Fourier sums”, Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S14–S20
3. N. Yu. Antonov, “Note on estimates for the growth order of sequences of multiple rectangular Fourier sums”, Proc. Steklov Inst. Math. (Suppl.), 277, suppl. 1 (2012), 4–8
4. N. Yu. Antonov, “Estimates for the growth order of sequences of multiple rectangular Fourier sums of integrable functions”, J. Math. Sci., 209:1 (2015), 1–11
•  Number of views: This page: 209 Full text: 79 References: 21

 Contact us: math-net2021_11 [at] mi-ras ru Terms of Use Registration to the website Logotypes © Steklov Mathematical Institute RAS, 2021