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Operators of Fourier typepwith respect to some subgroups of a locally compact Abelian group

✍ Scribed by Changsun Choi; Hun Hee Lee

Publisher
Springer
Year
2003
Tongue
English
Weight
169 KB
Volume
81
Category
Article
ISSN
0003-889X

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πŸ“œ SIMILAR VOLUMES

Fourier type 2 operators with respect to
Fourier type 2 operators with respect to locally compact abelian groups
✍ Aicke Hinrichs; Mariusz Piotrowski πŸ“‚ Article πŸ“… 2004 πŸ› John Wiley and Sons 🌐 English βš– 121 KB

## Abstract A linear and bounded operator __T__ between Banach spaces __X__ and __Y__ has Fourier type 2 with respect to a locally compact abelian group __G__ if there exists a constant __c__ > 0 such thatβˆ₯__T__$\hat f$βˆ₯~2~ ≀ __c__βˆ₯__f__βˆ₯~2~ holds for all __X__‐valued functions __f__ ∈ __L__^__X__^

Rearrangements of Functions on a Locally
Rearrangements of Functions on a Locally Compact Abelian Group and Integrability of the Fourier Transform
✍ A. Gulisashvili πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 524 KB

We find in this paper the equimeasurable hulls and kernels of some function classes on a locally compact abelian group. These classes consist of all functions for which the Fourier transform belongs to a given Lorentz space on the dual group. Different special cases of the problems considered in thi