# Irregular amalgams Academic Article

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### abstract

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

• 1986