On Lorentz spaces Γp,w
2004 (English)In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, no 140, 285-318 p.Article in journal (Refereed) Published
We study Lorentz spaces Γp,w where 0 < p < ∞, and w is a nonnegative measurable weight function. We first present some results concerning new formulas for the quasi-norm, duality, embeddings and Boyd indices. We then show that, whenever Γp,w does not coincide with L1 + L∞, it contains an order isomorphic and complemented copy of lp. We apply this result to determine criteria for order convexity and concavity as well as for lower and upper estimates. Finally, we characterize the type and cotype of Γp,w.
Place, publisher, year, edition, pages
2004. no 140, 285-318 p.
Research subject Mathematics
IdentifiersURN: urn:nbn:se:ltu:diva-7314DOI: 10.1007/BF02786637Local ID: 5a9c7730-aa2f-11db-aeba-000ea68e967bOAI: oai:DiVA.org:ltu-7314DiVA: diva2:980203
Validerad; 2004; 20070122 (kani)2016-09-292016-09-29Bibliographically approved