Irregular amalgams

James Stewart and Saleem Watson

International Journal of Mathematics and Mathematical Sciences, 1986, vol. 9, 1-10

Abstract:

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

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:809292

DOI: 10.1155/S0161171286000418

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