Discretization and anti-discretization of rearrangement-invariant norms

• Autores: Amiran Gogatishvili, Lubos Pick
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 47, Nº 2, 2003, págs. 311-358
• Idioma: inglés
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• Resumen

  • We develop a new method of discretization and anti-discretization of weighted inequalities which we apply to norms in classical Lorentz spaces and to spaces endowed with the so-called Hilbert norm. Main applications of our results include new integral conditions characterizing embeddings Γp(v)
    → Γq(w) and Γp(v)
    → Λq(w) and an integral characterization of the associate space to Γp(v), where p, q ∈ (0, ∞), v, w are weights on [0, ∞) and fΛp(v) = ∞ 0 f∗(t) pv(t) dt1/p, fΓp(v) = ∞ 0 f∗∗(t) pv(t) dt1/p.