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Lipschitz spaces with respect to Jacobi translation.

Math. Nachr. 284, 2312-2326 (2011)
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Open Access Green möglich sobald Postprint bei der ZB eingereicht worden ist.
The Jacobi polynomials induce a translation operator on function spaces on the interval [− 1, 1]. For any homogeneous Banach space B w.r.t. this translation, we can study the according little and big Lipschitz spaces, equation image and equation image respectively. The big Lipschitz spaces are not homogeneous themselves. Therefore we introduce semihomogeneous Banach spaces w.r.t. Jacobi translation, of which the big Lipschitz spaces are particular examples. We study the relation between semihomogeneous Banach spaces and their homogeneous counterparts. We give a characterisation of Lipschitz spaces in terms of intermediate spaces. Our main result is that, for an arbitrary homogeneous Banach space B, the bidual of the little Lipschitz space equation image is the corresponding big one, namely equation image
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter Jacobi polynomials; Jacobi translation operator; homogeneous Banach space; Lipschitz space; MSC (2010) 46E99; 41A10; 33C45
ISSN (print) / ISBN 0025-584X
e-ISSN 1522-2616
Quellenangaben Band: 284, Heft: 17-18, Seiten: 2312-2326 Artikelnummer: , Supplement: ,
Verlag Wiley
Begutachtungsstatus Peer reviewed