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Eurasian Math. J., 2017, Volume 8, Number 3, Pages 10–27 (Mi emj262)  

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

Net spaces on lattices, Hardy–Littlewood type inequalities, and their converses

R. Akylzhanov, M. Ruzhansky

Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, United Kingdom

Abstract: We introduce abstract net spaces on directed sets and prove their embedding and interpolation properties. Typical examples of interest are lattices of irreducible unitary representations of compact Lie groups and of class I representations with respect to a subgroup. As an application, we prove Hardy–Littlewood type inequalities and their converses on compact Lie groups and on compact homogeneous manifolds.

Keywords and phrases: net spaces, Lie groups, homogeneous manifolds, Hardy–Littlewood inequality.

Funding Agency Grant Number
Engineering and Physical Sciences Research Council EP/K039407/1
Leverhulme Trust RPG-2014-02


Full text: PDF file (501 kB)
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Bibliographic databases:
MSC: 35G10, 35L30, 46F05
Received: 27.02.2016
Revised: 10.02.2017
Language:

Citation: R. Akylzhanov, M. Ruzhansky, “Net spaces on lattices, Hardy–Littlewood type inequalities, and their converses”, Eurasian Math. J., 8:3 (2017), 10–27

Citation in format AMSBIB
\Bibitem{AkiRuz17}
\by R.~Akylzhanov, M.~Ruzhansky
\paper Net spaces on lattices, Hardy--Littlewood type inequalities, and their converses
\jour Eurasian Math. J.
\yr 2017
\vol 8
\issue 3
\pages 10--27
\mathnet{http://mi.mathnet.ru/emj262}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3719791}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000416973500003}


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    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. R. Akylzhanov, M. Ruzhansky, E. Nursultanov, “Hardy-littlewood, Hausdorff-young-paley inequalities, and l-p- l-q fourier multipliers on compact homogeneous manifolds”, J. Math. Anal. Appl., 479:2 (2019), 1519–1548  crossref  mathscinet  zmath  isi  scopus
    2. R. Daher, J. Delgado, M. Ruzhansky, “Titchmarsh theorems for fourier transforms of holder-lipschitz functions on compact homogeneous manifolds”, Mon.heft. Math., 189:1 (2019), 23–49  crossref  mathscinet  zmath  isi  scopus
  • Eurasian Mathematical Journal
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