Geodesic
Spaces defined by the level function and their duals
Studia Mathematica, Tome 111 (1994) no. 1, pp. 19-52

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The classical level function construction of Halperin and Lorentz is extended to Lebesgue spaces with general measures. The construction is also carried farther. In particular, the level function is considered as a monotone map on its natural domain, a superspace of $L^p$. These domains are shown to be Banach spaces which, although closely tied to $L^p$ spaces, are not reflexive. A related construction is given which characterizes their dual spaces.
DOI : 10.4064/sm-111-1-19-52
Keywords: function spaces, Hölder's inequality, Hardy's inequality, dual spaces

Gord Sinnamon 1

1 
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Gord Sinnamon. Spaces defined by the level function and their duals. Studia Mathematica, Tome 111 (1994) no. 1, pp. 19-52. doi: 10.4064/sm-111-1-19-52

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