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., 2019, Volume 210, Number 8, Pages 67–86 (Mi msb9099)  

On maximizers of a convolution operator in $L_p$-spaces

G. V. Kalacheva, S. Yu. Sadovb

a Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
b Moscow, Russia

Abstract: The paper is concerned with convolution operators in $\mathbb R^d$, whose kernels are in $L_q$, which act from $L_p$ into $L_s$, where $1/p+1/q=1+1/s$. It is shown that for $1<q,p,s<\infty$ there exists a maximizer (a function with $L_p$-norm $1$) at which the supremum of the $s$-norm of the convolution is attained. A special analysis is carried out for the cases in which one of the exponents $q,p$, or $s$ is $1$ or $\infty$.
Bibliography: 12 titles.

Keywords: convolution, Young inequality, existence of an extremal function, tight sequence, concentration compactness.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm9099

Full text: PDF file (811 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2019, 210:8, 1129–1147

Bibliographic databases:

UDC: 517.44+517.972.4
MSC: 44A35, 46E30, 49J99
Received: 18.03.2018 and 16.01.2019

Citation: G. V. Kalachev, S. Yu. Sadov, “On maximizers of a convolution operator in $L_p$-spaces”, Mat. Sb., 210:8 (2019), 67–86; Sb. Math., 210:8 (2019), 1129–1147

Citation in format AMSBIB
\Bibitem{KalSad19}
\by G.~V.~Kalachev, S.~Yu.~Sadov
\paper On maximizers of a~convolution operator in $L_p$-spaces
\jour Mat. Sb.
\yr 2019
\vol 210
\issue 8
\pages 67--86
\mathnet{http://mi.mathnet.ru/msb9099}
\crossref{https://doi.org/10.4213/sm9099}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2019SbMat.210.1129K}
\elib{http://elibrary.ru/item.asp?id=38593081}
\transl
\jour Sb. Math.
\yr 2019
\vol 210
\issue 8
\pages 1129--1147
\crossref{https://doi.org/10.1070/SM9099}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000508164100003}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85087443480}


Linking options:
  • http://mi.mathnet.ru/eng/msb9099
  • https://doi.org/10.4213/sm9099
  • http://mi.mathnet.ru/eng/msb/v210/i8/p67

    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
  • Математический сборник Sbornik: Mathematics (from 1967)
    Number of views:
    This page:146
    References:19
    First page:19

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