A characterization of Lorentz-improving measures

• Grinnell, Raymond J. ^[1]
  1. [1] University of the West Indies

     University of the West Indies

     Jamaica

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 14, Nº. 1, 1995, págs. 43-50
• Idioma: inglés
• DOI: 10.22199/S07160917.1995.0001.00004
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• Resumen

  • Let G be an infinite compact abelian group and let Ꞅ denote its dual group. A borel measure µ on G is called Lorentz-improving if there existe p, q1, and q2, where 1 < p < ꝏ and 1 ≤ q1 ≤ q2 ≤ ꝏ, such that µ * L (p, q2) ⊆  L (p, q1). A detailed exposition of our recent characterization of Lorentz-improving measures is presented here. In this result Lorentz-improving measures are characterized in terms of the size of the sets {ϒ ∊ Ꞅ : │ µ (ϒ) │  > ∊ } and in terms of n-fold convolution powers. This characterization is analogous to a known characterization of LP-improving measures due to Hare.

• Referencias bibliográficas
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