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



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Sb., 2009, Volume 200, Number 2, Pages 89–106 (Mi msb4510)  

This article is cited in 2 scientific papers (total in 2 papers)

Some summability methods for power series of functions in $H^p(D^n)$, $0<p<\infty$

S. G. Pribegin

Odessa National Maritime University

Abstract: Let $H^p(D^n)$ be a Hardy space in the unit polydisc
$$ D^n=ż\in\mathbb C^n:|z_j|<1, j=1,…,n\} $$
and let
$$ R^{l,\alpha}_\varepsilon(f,e^{i\theta})=\sum_k(1-(\varepsilon|k|)^l)^\alpha_+\widehat f_ke^{ik\theta}, \qquad l>0, \quad \alpha>0, $$
be the generalized Riesz means of a function $f\in H^p(D^n)$. For certain standard relations between $p$, $l$, $n$ and $\alpha$ the following estimate is established:
$$ C_1(\alpha,l,p)\widetilde{\omega}_l(\varepsilon,f)_p \le\|f(e^{i\theta})-R_\varepsilon^{l,\alpha}(f,e^{i\theta})\|_p \le C_2(\alpha,l,p)\omega_l(\varepsilon,f)_p, $$
where $\widetilde\omega_l(\varepsilon,f)_p$ and $\omega_l(\varepsilon,f)_p$ are integral moduli of continuity of order $l$.
Bibliography: 13 titles.

Keywords: series' means, generalized Riesz means, generalized Abel-Poisson means, right fractional Riemann-Liouville integral, right fractional derivative.

DOI: https://doi.org/10.4213/sm4510

Full text: PDF file (575 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2009, 200:2, 243–260

Bibliographic databases:

UDC: 517.550.2
MSC: 41A25, 42B30
Received: 04.07.2005 and 27.11.2008

Citation: S. G. Pribegin, “Some summability methods for power series of functions in $H^p(D^n)$, $0<p<\infty$”, Mat. Sb., 200:2 (2009), 89–106; Sb. Math., 200:2 (2009), 243–260

Citation in format AMSBIB
\Bibitem{Pri09}
\by S.~G.~Pribegin
\paper Some summability methods for power series of functions in $H^p(D^n)$, $0<p<\infty$
\jour Mat. Sb.
\yr 2009
\vol 200
\issue 2
\pages 89--106
\mathnet{http://mi.mathnet.ru/msb4510}
\crossref{https://doi.org/10.4213/sm4510}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2503139}
\zmath{https://zbmath.org/?q=an:1173.41009}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2009SbMat.200..243P}
\elib{http://elibrary.ru/item.asp?id=19066109}
\transl
\jour Sb. Math.
\yr 2009
\vol 200
\issue 2
\pages 243--260
\crossref{https://doi.org/10.1070/SM2009v200n02ABEH003994}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000266224500010}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-67650896326}


Linking options:
  • http://mi.mathnet.ru/eng/msb4510
  • https://doi.org/10.4213/sm4510
  • http://mi.mathnet.ru/eng/msb/v200/i2/p89

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. Yu. S. Kolomoitsev, “Approximation properties of generalized Bochner-Riesz means in the Hardy spaces $H_p$, $0<p\le 1$”, Sb. Math., 203:8 (2012), 1151–1168  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. S. G. Pribegin, “Cesàro means for the functions from the Hardy space in polydisc”, Russian Math. (Iz. VUZ), 59:4 (2015), 46–49  mathnet  crossref
  • Математический сборник Sbornik: Mathematics (from 1967)
    Number of views:
    This page:591
    Full text:117
    References:27
    First page:20

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020