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



Ufimsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






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


Ufimsk. Mat. Zh., 2013, Volume 5, Issue 1, Pages 3–10 (Mi ufa182)  

This article is cited in 1 scientific paper (total in 1 paper)

Compactness criterion for fractional integration operator of infinitesimal order

A. M. Abylayeva, A. O. Baiarystanov

L. N. Gumilev Eurasian National University, Astana

Abstract: We obtain necessary and sufficient conditions of compactness for the operator
$$Kf(x)=\int\limits_{0}^{x}\ln\frac{x}{x-s}\frac{f(s)}{s}ds$$
from $L_{p,v}$ in $L_{q,u}$ at $1<p\leq q<\infty$ and $v(x)=x^{-\gamma}$, $\gamma>0$, where $L_{q,u}$ is the set of all measurable on $(0, \infty)$ functions $f$ with finite norm $\|uf\|_{q}$.

Keywords: compactness, fractional integration operator, Riemann–Liouville operator, singular operator, adjoint operator, Holder inequality, weighted inequalities.

Full text: PDF file (403 kB)
References: PDF file   HTML file

English version:
Ufa Mathematical Journal, 2013, 5:1, 3–10 (PDF, 291 kB); https://doi.org/10.13108/2013-5-1-3

Bibliographic databases:

UDC: 517.518
Received: 23.12.2011

Citation: A. M. Abylayeva, A. O. Baiarystanov, “Compactness criterion for fractional integration operator of infinitesimal order”, Ufimsk. Mat. Zh., 5:1 (2013), 3–10; Ufa Math. J., 5:1 (2013), 3–10

Citation in format AMSBIB
\Bibitem{AbyBai13}
\by A.~M.~Abylayeva, A.~O.~Baiarystanov
\paper Compactness criterion for fractional integration operator of infinitesimal order
\jour Ufimsk. Mat. Zh.
\yr 2013
\vol 5
\issue 1
\pages 3--10
\mathnet{http://mi.mathnet.ru/ufa182}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3429946}
\elib{http://elibrary.ru/item.asp?id=18929622}
\transl
\jour Ufa Math. J.
\yr 2013
\vol 5
\issue 1
\pages 3--10
\crossref{https://doi.org/10.13108/2013-5-1-3}


Linking options:
  • http://mi.mathnet.ru/eng/ufa182
  • http://mi.mathnet.ru/eng/ufa/v5/i1/p3

    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. A. M. Abylayeva, L.-E. Persson, “Hardy type inequalities and compactness of a class of integral operators with logarithmic singularities”, Math. Inequal. Appl., 21:1 (2018), 201–215  crossref  mathscinet  zmath  isi  scopus
  • Уфимский математический журнал
    Number of views:
    This page:271
    Full text:91
    References:45
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019