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Are generalized Lorentz "spaces" really spaces?
Department of Mathematics, Technion - Israel Institute of Technology.
University of Memphis.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
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.
Mathematics
##### Identifiers
Local ID: 1f760710-a643-11db-9811-000ea68e967bOAI: oai:DiVA.org:ltu-4097DiVA: diva2:976960
##### Note
Validerad; 2004; 20070117 (kani)Available from: 2016-09-29 Created: 2016-09-29Bibliographically approved

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Maligranda, Lech
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