International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 2, Pages 331-340
doi:10.1155/S0161171286000418

Irregular amalgams

James Stewart1 and Saleem Watson2

1Department of Mathematics, McMaster University, Hamilton L8S 4K1, Ontario, Canada
 2Department of Mathematics, Pennsylvania State University, Media 19063, Pennsylvania, USA

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,ℓq)α. In particular, we study how (Lp,ℓq)α varies as p, q, and α vary and determine conditions under which translation is continuous.