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.