Rearrangement-Invariant Spaces of Functions on LCA Groups

✍ Scribed by Archil Gulisashvili

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 343 KB
• Volume: 156
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1998.3266

✦ Synopsis

In this paper the rearrangement-invariant hulls and kernels of the classes

loc ] on a noncompact nondiscrete locally compact abelian group are characterized. The space L 1 loc & S$ of tempered distributions serves as the extended domain of the Fourier transform instead of the classical domain L 1 +L 2 . We also introduce and study a new function space P 0 which arises as the rearrangement-invariant hull of some of the classes under consideration.