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Are generalized Lorentz "spaces" really spaces?
Department of Mathematics, Technion - Israel Institute of Technology.
University of Memphis.
LuleƄ University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0002-9584-4083
Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovsk.
2004 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 132, no 12, 3615-3625 p.Article in journal (Refereed) Published
Abstract [en]

Let $w$ be a non-negative measurable function on $(0,\infty)$, non-identically zero, such that $W(t)=\int_0^tw(s)ds<\infty$ for all $t>0$. The authors study conditions on $w$ for the Lorentz spaces $\Lambda^p(w)$ and $\Lambda^{p,\infty}(w)$, defined by the conditions $\int_0^\infty (f^*(t))^pw(t)dt<\infty$ and $\sup_{00,$$ it is shown that, if $\varphi$ satisfies the $\Delta_2$-condition and $w>0$, then $\Lambda_{\varphi,w}$ is a linear space if and only if $W$ satisfies the $\Delta_2$-condition.

Place, publisher, year, edition, pages
2004. Vol. 132, no 12, 3615-3625 p.
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-4097DOI: 10.1090/S0002-9939-04-07477-5Local ID: 1f760710-a643-11db-9811-000ea68e967bOAI: oai:DiVA.org:ltu-4097DiVA: diva2:976960
Note
Validerad; 2004; 20070117 (kani)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

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