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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Some necessary conditions for radial Fourier multipliers


Author: Walter Trebels
Journal: Proc. Amer. Math. Soc. 58 (1976), 97-103
MSC: Primary 42A18
DOI: https://doi.org/10.1090/S0002-9939-1976-0412716-8
MathSciNet review: 0412716
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Abstract: Necessary conditions in terms of differentiability and growth properties for a radial function $ m(\vert z\vert)$ to be a Fourier multiplier of type $ (p,q)$ are given and compared with sufficient ones.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0412716-8
Keywords: Radial Fourier multipliers, fractional differentiation
Article copyright: © Copyright 1976 American Mathematical Society