Irregular amalgams

[摘要] The amalgam ofLpandℓqconsists of those functions for which the sequence ofLp-norms over the intervals[n,n+1)is inℓq. These spaces(Lp,ℓq)have been studied in several recent papers. Here we replace the intervals[n,n+1)by a coverα={In;n∈Z}of the real line consisting of disjoint half-open intervalsIneach 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)αvaries asp,q, andαvary and determine conditions under which translation is continuous.

[学科分类] 数学（综合）