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ArticleOriginal scientific text

Title

Spaces defined by the level function and their duals

Authors 1

Affiliations

  1. Department of Mathematics, University of Western Ontario, London, Ontario, N6A 5B7, Canada

Abstract

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 Lp. These domains are shown to be Banach spaces which, although closely tied to Lp spaces, are not reflexive. A related construction is given which characterizes their dual spaces.

Keywords

ENG
function spaces, Hölder's inequality, Hardy's inequality, dual spaces

Bibliography

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Studia Mathematica
1994/111/1
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Pages:
19-52
Main language of publication
English
Received
1993-07-16
Published
1994
Exact and natural sciences