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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Best constants for two nonconvolution inequalities


Authors: Michael Christ and Loukas Grafakos
Journal: Proc. Amer. Math. Soc. 123 (1995), 1687-1693
MSC: Primary 42B25; Secondary 26D15, 47B38
MathSciNet review: 1239796
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Abstract: The norm of the operator which averages $ \vert f\vert$ in $ {L^p}({\mathbb{R}^n})$ over balls of radius $ \delta \vert x\vert$ centered at either 0 or x is obtained as a function of n , p and $ \delta $. Both inequalities proved are n-dimensional analogues of a classical inequality of Hardy in $ {\mathbb{R}^1}$. Finally, a lower bound for the operator norm of the Hardy-Littlewood maximal function on $ {L^p}({\mathbb{R}^n})$ is given.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1239796-6
PII: S 0002-9939(1995)1239796-6
Article copyright: © Copyright 1995 American Mathematical Society