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On Lorentz spaces Γp,w
University of Memphis.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0002-9584-4083
2004 (English)In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, no 140, 285-318 p.Article in journal (Refereed) Published
Abstract [en]

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.
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-7314DOI: 10.1007/BF02786637Local ID: 5a9c7730-aa2f-11db-aeba-000ea68e967bOAI: oai:DiVA.org:ltu-7314DiVA: diva2:980203
Note
Validerad; 2004; 20070122 (kani)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

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