On Lorentz spaces Γ p,w | Zendy

Anna Kamińska | Zendy; Lech Maligranda | Zendy

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On Lorentz spaces Γ p,w

Author(s) -

Anna Kamińska,

Lech Maligranda

Publication year - 2004

Publication title -

israel journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.168

H-Index - 63

eISSN - 1565-8511

pISSN - 0021-2172

DOI - 10.1007/bf02786637

Subject(s) - mathematics , convexity , lorentz transformation , lorentz space , order (exchange) , duality (order theory) , norm (philosophy) , combinatorics , type (biology) , function (biology) , pure mathematics , physics , classical mechanics , ecology , finance , evolutionary biology , political science , financial economics , law , economics , biology

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.Validerad; 2004; 20070122 (kani

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