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arXiv · 1510.01251

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

Rauan Akylzhanov·Michael Ruzhansky
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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.

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Rauan Akylzhanov, Michael Ruzhansky. 2015-10-05. Net spaces on lattices, Hardy-Littlewood type inequalities, and their converses. https://arxiv.org/abs/1510.01251

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