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On Lorentz spaces Γ p,w

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Abstract

We study Lorentz spaces Γ p,w , where 0<p<∞, andw 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 Γ p,w does not coincide withL 1+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 Γ p,w .

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, The University of Memphis, 38152, Memphis, TN, USA

    Anna Kamińska

  2. Department of Mathematics, Luleå University of Technology, SE-971 87, Luleå, Sweden

    Lech Maligranda

Authors
  1. Anna Kamińska
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  2. Lech Maligranda
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Additional information

Research partially supported by a grant from the Swedish Natural Science Research Council (Ö-AH/KG 08685-314).

Research supported by a grant from the Swedish Natural Science Research Council (M5105-20005228/2000).

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Kamińska, A., Maligranda, L. On Lorentz spaces Γ p,w . Isr. J. Math. 140, 285–318 (2004). https://doi.org/10.1007/BF02786637

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  • DOI: https://doi.org/10.1007/BF02786637

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