Duality of Fourier type with respect to locally compact Abelian groups |
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| Authors: | Aicke Hinrichs Hun Hee Lee |
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| Institution: | (1) Department of Mathematics, Friedrich-Schiller-University Jena, Ernst-Abbe-Platz 1-4, D-07743, Germany;(2) Department of Mathematical Sciences, Seoul National University, San56-1 Shinrim-dong Kwanak-gu, Seoul, 151-747, Republic of Korea |
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| Abstract: | It is shown that a Banach space X has Fourier type p with respect to a locally compact abelian group G if and only if the dual space X′ has Fourier type p with respect to G if and only if X has Fourier type p with respect to the dual group of G. This extends previously known results for the classical groups and the Cantor group to the setting of general locally compact
abelian groups.
Supported by DFG grant Hi 584/2-2.
Partially supported by a DAAD-grant A/02/46571. |
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