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

2015/10/05 by Rauan Akylzhanov, Michael Ruzhansky, Akylzhanov, Rauan +1
Mathematics · #20G05 #46E30 (Primary) 22C05 (Secondary) #Advanced Algebra and Geometry #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1510.01251

openalex publication_date 2015/10/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• Hardy-Littlewood, Hausdorff-Young-Paley inequalities, and Lp-Lq Fourier multipliers on compact homogeneous manifolds

Related

• Interpolation properties of certain classes of net spaces
• Hölder inequality for symmetric operator spaces and trace property of K-cycles
• Hardy's theorem for compact Lie groups
• Measure theory and classifying spaces
• On orbit spaces of representations of compact Lie groups