Duality of ODE-determined norms

• Jarno Talponen ^[1]
  1. [1] University of Eastern Finland

     University of Eastern Finland

     Kuopio, Finlandia

     
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 124, Nº 1, 2019, págs. 61-80
• Idioma: inglés
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• Resumen

  • Recently the author initiated a novel approach to varying exponent Lebesgue space Lp(⋅) norms. In this approach the norm is defined by means of weak solutions to suitable first order ordinary differential equations (ODE). The resulting norm is equivalent with constant 2 to a corresponding Nakano norm but the norms do not coincide in general and thus their isometric properties are different. In this paper the duality of these ODE-determined Lp(⋅) spaces is investigated. It turns out that the duality of the classical Lp spaces generalizes nicely to this class of spaces. Here the duality pairing and Hölder's inequality work in the isometric sense which is a notable feature of these spaces. The uniform convexity and smoothness of these spaces are characterized under the anticipated conditions. A kind of universal space construction is also given for these spaces