Rearrangement-Invariant Spaces of Functions on LCA Groups

In this paper the rearrangement-invariant hulls and kernels of the classes {f:f∈Lp} and {f:f∈L1loc} on a noncompact nondiscrete locally compact abelian group are characterized. The spaceL1loc∩S′ of tempered distributions serves as the extended domain of the Fourier transform instead of the classical...

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Bibliographic Details
Published in:Journal of functional analysis 1998-07, Vol.156 (2), p.384-410
Main Author: Gulisashvili, Archil
Format: Article
Language:English
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Summary:In this paper the rearrangement-invariant hulls and kernels of the classes {f:f∈Lp} and {f:f∈L1loc} on a noncompact nondiscrete locally compact abelian group are characterized. The spaceL1loc∩S′ of tempered distributions serves as the extended domain of the Fourier transform instead of the classical domainL1+L2. We also introduce and study a new function spaceP0which arises as the rearrangement-invariant hull of some of the classes under consideration.
ISSN:0022-1236
1096-0783
DOI:10.1006/jfan.1998.3266