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Rearrangements of Functions on a Locally Compact Abelian Group and Integrability of the Fourier Transform

โœ Scribed by A. Gulisashvili

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
524 KB
Volume
146
Category
Article
ISSN
0022-1236

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โœฆ Synopsis

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 this paper have been originally studied by Hardy, Littlewood, Hewitt, Ross, Cereteli, and the author. 1997 Academic Press Problems A and B were originally studied for the circle group T and the group of integers Z by Hardy and Littlewood [HL1, HL2] (see also [Z], Ch. 11). In the case G=Z, some modifications should be made in the formulation of the problems (see the definition of classes A p, q and A p, q below). Hardy and Littlewood solved Problem A in the case 1< p<2 and article no.

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โœ Eberhard Kaniuth; Anthony T. Lau ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 174 KB

For a closed subgroup H of a locally compact group G consider the property that the continuous positive definite functions on G which are identically one on H separate points in G"H from points in H. We prove a structure theorem for almost connected groups having this separation property for every c