Matematicheskie Zametki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



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






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


Matematicheskie Zametki, 2016, Volume 100, Issue 1, Pages 47–58
DOI: https://doi.org/10.4213/mzm11159
(Mi mzm11159)
 

This article is cited in 13 scientific papers (total in 13 papers)

Mixed Norm Bergman–Morrey-type Spaces on the Unit Disc

A. N. Karapetyantsab, S. G. Samkoc

a Southern Federal University, Rostov-on-Don
b Don State Technical University, Rostov-on-Don
c Universidade do Algarve, Portugal
References:
Abstract: We introduce and study the mixed-norm Bergman–Morrey space $\mathscr A^{q;p,\lambda}(\mathbb D)$, mixed-norm Bergman–Morrey space of local type $\mathscr A_{\mathrm{loc}}^{q;p,\lambda}(\mathbb D)$, and mixed-norm Bergman–Morrey space of complementary type ${^{\complement}\!}\mathscr A^{q;p,\lambda}(\mathbb D)$ on the unit disk $\mathbb D$ in the complex plane $\mathbb C$. The mixed norm Lebesgue–Morrey space $\mathscr L^{q;p,\lambda}(\mathbb D)$ is defined by the requirement that the sequence of Morrey $L^{p,\lambda}(I)$-norms of the Fourier coefficients of a function $f$ belongs to $l^q$ ($I=(0,1)$). Then, $\mathscr A^{q;p,\lambda}(\mathbb D)$ is defined as the subspace of analytic functions in $\mathscr L^{q;p,\lambda}(\mathbb D)$. Two other spaces $\mathscr A_{\mathrm{loc}}^{q;p,\lambda}(\mathbb D)$ and ${^{\complement}\!}\mathscr A^{q;p,\lambda}(\mathbb D)$ are defined similarly by using the local Morrey $L_{\mathrm{loc}}^{p,\lambda}(I)$-norm and the complementary Morrey ${^{\complement}\!}L^{p,\lambda}(I)$-norm respectively. The introduced spaces inherit features of both Bergman and Morrey spaces and, therefore, we call them Bergman–Morrey-type spaces. We prove the boundedness of the Bergman projection and reveal some facts on equivalent description of these spaces.
Keywords: Bergman–Morrey-type space, mixed norm.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-02732
S. G. Samko's work was supported by the Russian Foundation for Basic Research under grant 15-01-02732.
Received: 17.02.2016
English version:
Mathematical Notes, 2016, Volume 100, Issue 1, Pages 38–48
DOI: https://doi.org/10.1134/S000143461607004X
Bibliographic databases:
Document Type: Article
UDC: 517.53
Language: Russian
Citation: A. N. Karapetyants, S. G. Samko, “Mixed Norm Bergman–Morrey-type Spaces on the Unit Disc”, Mat. Zametki, 100:1 (2016), 47–58; Math. Notes, 100:1 (2016), 38–48
Citation in format AMSBIB
\Bibitem{KarSam16}
\by A.~N.~Karapetyants, S.~G.~Samko
\paper Mixed Norm Bergman--Morrey-type Spaces on the Unit Disc
\jour Mat. Zametki
\yr 2016
\vol 100
\issue 1
\pages 47--58
\mathnet{http://mi.mathnet.ru/mzm11159}
\crossref{https://doi.org/10.4213/mzm11159}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3588827}
\elib{https://elibrary.ru/item.asp?id=26414276}
\transl
\jour Math. Notes
\yr 2016
\vol 100
\issue 1
\pages 38--48
\crossref{https://doi.org/10.1134/S000143461607004X}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000382193300004}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84983770619}
Linking options:
  • https://www.mathnet.ru/eng/mzm11159
  • https://doi.org/10.4213/mzm11159
  • https://www.mathnet.ru/eng/mzm/v100/i1/p47
  • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024