International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1986 / Article

Open Access

Volume 9 |Article ID 809292 |

James Stewart, Saleem Watson, "Irregular amalgams", International Journal of Mathematics and Mathematical Sciences, vol. 9, Article ID 809292, 10 pages, 1986.

Irregular amalgams

Received17 Jul 1985


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

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.

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