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International Journal of Mathematics and Mathematical Sciences - Volume 9 1986, Issue 2, Pages 331-340



Department of Mathematics, McMaster University, Hamilton, Ontario L8S 4K1, Canada

Department of Mathematics, Pennsylvania State University, Media, Pennsylvania 19063, USA

Received 17 July 1985

Copyright © 1986 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The amalgam of Lp and ℓq consists of those functions for which the sequence of Lp-norms over the intervals n,n+1 is in ℓq. These spaces Lp,ℓq have been studied in several recent papers. Here we replace the intervals n,n+1 by a cover α={In;n∈Z} of the real line consisting of disjoint half-open intervals In each of the form a,b, and investigate which properties of Lp,ℓq carry over to these irregular amalgams Lp,ℓqα. In particular, we study how Lp,ℓqα varies as p, q, and α vary and determine conditions under which translation is continuous.





Autor: James Stewart and Saleem Watson

Fuente: https://www.hindawi.com/



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