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

R Akylzhanov and Michael Ruzhansky (UGent)
(2017) EURASIAN MATHEMATICAL JOURNAL. 8(3). p.10-27
Author
Organization
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
net spaces, Lie groups, homogeneous manifolds, Hardy-Littlewood inequality, COMPACT LIE-GROUPS, NIKOLSKII INEQUALITY

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MLA
Akylzhanov, R., and Michael Ruzhansky. “Net Spaces on Lattices, Hardy-Littlewood Type Inequalities, and Their Converses.” EURASIAN MATHEMATICAL JOURNAL, vol. 8, no. 3, 2017, pp. 10–27.
APA
Akylzhanov, R., & Ruzhansky, M. (2017). Net spaces on lattices, Hardy-Littlewood type inequalities, and their converses. EURASIAN MATHEMATICAL JOURNAL, 8(3), 10–27.
Chicago author-date
Akylzhanov, R, and Michael Ruzhansky. 2017. “Net Spaces on Lattices, Hardy-Littlewood Type Inequalities, and Their Converses.” EURASIAN MATHEMATICAL JOURNAL 8 (3): 10–27.
Chicago author-date (all authors)
Akylzhanov, R, and Michael Ruzhansky. 2017. “Net Spaces on Lattices, Hardy-Littlewood Type Inequalities, and Their Converses.” EURASIAN MATHEMATICAL JOURNAL 8 (3): 10–27.
Vancouver
1.
Akylzhanov R, Ruzhansky M. Net spaces on lattices, Hardy-Littlewood type inequalities, and their converses. EURASIAN MATHEMATICAL JOURNAL. 2017;8(3):10–27.
IEEE
[1]
R. Akylzhanov and M. Ruzhansky, “Net spaces on lattices, Hardy-Littlewood type inequalities, and their converses,” EURASIAN MATHEMATICAL JOURNAL, vol. 8, no. 3, pp. 10–27, 2017.
@article{8585434,
  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.}},
  author       = {{Akylzhanov, R and Ruzhansky, Michael}},
  issn         = {{2077-9879}},
  journal      = {{EURASIAN MATHEMATICAL JOURNAL}},
  keywords     = {{net spaces,Lie groups,homogeneous manifolds,Hardy-Littlewood inequality,COMPACT LIE-GROUPS,NIKOLSKII INEQUALITY}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{10--27}},
  title        = {{Net spaces on lattices, Hardy-Littlewood type inequalities, and their converses}},
  volume       = {{8}},
  year         = {{2017}},
}