RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



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






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


Sibirsk. Mat. Zh., 2018, Volume 59, Number 1, Pages 158–170 (Mi smj2962)  

Sobolev embedding theorems and generalizations for functions on a metric measure space

N. N. Romanovskiĭ

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: Considering the metric case, we define an analog of the Sobolev space of functions with generalized derivatives of order greater than 1. The space of functions with fractional generalized derivatives is also treated. We prove generalizations of the Sobolev embedding theorems and Gagliardo–Nirenberg interpolation inequalities to the metric case.

Keywords: Sobolev classes, metric measure space, embedding theorems, Gagliardo–Nirenberg inequalities.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00801
The author was supported by the Russian Foundation for Basic Research (Grant 17-01-00801).


DOI: https://doi.org/10.17377/smzh.2018.59.114

Full text: PDF file (332 kB)
References: PDF file   HTML file

English version:
Siberian Mathematical Journal, 2018, 59:1, 126–135

Bibliographic databases:

UDC: 517.518+517.518.23
MSC: 35R30
Received: 06.07.2017

Citation: N. N. Romanovskiǐ, “Sobolev embedding theorems and generalizations for functions on a metric measure space”, Sibirsk. Mat. Zh., 59:1 (2018), 158–170; Siberian Math. J., 59:1 (2018), 126–135

Citation in format AMSBIB
\Bibitem{Rom18}
\by N.~N.~Romanovski{\v\i}
\paper Sobolev embedding theorems and generalizations for functions on a~metric measure space
\jour Sibirsk. Mat. Zh.
\yr 2018
\vol 59
\issue 1
\pages 158--170
\mathnet{http://mi.mathnet.ru/smj2962}
\crossref{https://doi.org/10.17377/smzh.2018.59.114}
\elib{http://elibrary.ru/item.asp?id=32824598}
\transl
\jour Siberian Math. J.
\yr 2018
\vol 59
\issue 1
\pages 126--135
\crossref{https://doi.org/10.1134/S0037446618010147}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000427144300014}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85043498124}


Linking options:
  • http://mi.mathnet.ru/eng/smj2962
  • http://mi.mathnet.ru/eng/smj/v59/i1/p158

    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
  • Сибирский математический журнал Siberian Mathematical Journal
    Number of views:
    This page:62
    Full text:6
    References:13
    First page:3

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