Discretization and anti-discretization of rearrangement-invariant norms
By Amiran Gogatishvili, L. Pick. 2003
107 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/1220d4fdd2dfec9b20e12877168768e9019a99fc
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In Applied Mathematics
- Joaquim Martín
- María J. Carro
- Amiran Gogatishvili
- Gord Sinnamon
- Tengiz Kopaliani
- Maria Rosaria Formica
Citations in the corpus
- WEIGHTED INEQUALITIES INVOLVING TWO HARDY OPERATORS WITH APPLICATIONS TO EMBEDDINGS OF FUNCTION SPACES (2008, methodology): “Since 1990, an enormous effort has been spent by many authors in the hunt of a characterization of embeddings between classical Lorentz spaces of both types L and G. Thanks to this extensive research powerful new techniques and methods were developed, and most of the desired characterizations have b”
- Characterization of interpolation between Grand, small or classical Lebesgue spaces (2017, background): “♦ For the lower bound, we need few lemmas The first lemma is a consequence of a general lemma given in Goldman Heinig and Stepanov ([20], see also [19] Lemma 3.”
- Transferring monotonicity in weighted norm inequalities (2003, background): “concave functions. It is well known, see for example [12, Lemma 2.3], that every quasi-concave function is equivalent to an increasing limit of functions in the image II∗(L+ λ ). Work of [ 5 , 6, 12] has characterized weighted Lebesgue space imbeddings of”