摘要
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;nεZ} 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.
關鍵字
amalgam延伸閱讀
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