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Abstract duality Sawyer formula and its applications

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Abstract.

The main subject of this paper is to present some general results on duality and Banach envelopes of a large class of symmetric quasi-Banach spaces. An abstract duality formula, a general form of the Sawyer’s characterization of the reverse Hölder inequality for L p -spaces, 1 < p < ∞, in function ideals is proved. This formula is then applied for characterization of Köthe duals of rearrangement invariant (r.i.) function lattices. A duality formula for 1-concave quasi-Banach function lattices is shown and it is employed to characterize Banach envelopes of r.i. quasi-Banach lattices. As applications of the duality formulas to quasi-normed Orlicz-Lorentz spaces, a description of their Köthe duals and of their Banach envelopes is presented. The conditions for normability as well as for boundedness of Hardy-Littlewood maximal operator are also given in some class of Orlicz-Lorentz spaces.

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Authors and Affiliations

  1. The University of Memphis, Memphis, TN, USA

    Anna Kamińska

  2. A. Mickiewicz University and Polish Academy of Sciences, Poznań, Poland

    Mieczysław Mastyło

Authors
  1. Anna Kamińska
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  2. Mieczysław Mastyło
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Additional information

The first author supported by NATO Grant CRG 972918.

The second author supported by KBN Grant 1 P03A 013 26 and NATO grant CRG 972918.

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Kamińska, A., Mastyło, M. Abstract duality Sawyer formula and its applications. Mh Math 151, 223–245 (2007). https://doi.org/10.1007/s00605-007-0445-9

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