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
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.
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MSC: 35G10, 35L30, 46F05
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
\by R.~Akylzhanov, M.~Ruzhansky
\paper Net spaces on lattices, Hardy--Littlewood type inequalities, and their converses
\jour Eurasian Math. J.
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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
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
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