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Proceedings of the American Mathematical Society

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

 

 

Convolution of $ L(p,\,q)$ functions


Author: Anthony P. Blozinski
Journal: Proc. Amer. Math. Soc. 32 (1972), 237-240
MSC: Primary 44.25
DOI: https://doi.org/10.1090/S0002-9939-1972-0288526-8
MathSciNet review: 0288526
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Abstract: In the present paper, examples are given to show that the convolution theorem, which is the $ L(p,q)$ analogue of Young's inequality for the $ {L^p}$ spaces, is best possible. This result is then used to obtain a theorem about bounded linear translation invariant operators between two $ L(p,q)$ spaces.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0288526-8
Keywords: $ L(p,q)$ spaces, convolution, convolution theorem, Young's inequality, translation invariant operator, locally compact group
Article copyright: © Copyright 1972 American Mathematical Society