Discretization and anti-discretization of rearrangement-invariant norms
Copyright policy )Discretization and anti-discretization of rearrangement-invariant norms
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.
Duality theorems, Classical Lorentz space, Inequalities involving derivatives and differential and integral operators, classical Lorentz space, Discretizing sequence, discretizing sequence, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Hilbert norm
Duality theorems, Classical Lorentz space, Inequalities involving derivatives and differential and integral operators, classical Lorentz space, Discretizing sequence, discretizing sequence, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Hilbert norm
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