Corpus ID: 119317252

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

  title={Net spaces on lattices, Hardy-Littlewood type inequalities, and their converses},
  author={R. Akylzhanov and M. Ruzhansky},
  journal={arXiv: Functional Analysis},
  • R. Akylzhanov, M. Ruzhansky
  • Published 2015
  • Mathematics
  • arXiv: Functional Analysis
  • 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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