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Remarks on the Hardy–Littlewood maximal function

Published online by Cambridge University Press:  14 November 2011

J. M. Aldaz
J. M. Aldaz
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain E-mail: [email protected]
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Extract

We answer questions of A. Carbery, M. Trinidad Menárguez and F. Soria by proving, firstly, that for the centred Hardy–Littlewood maximal function on the real line, the best constant C for the weak type (1, 1) inequality is strictly larger than 3/2, and secondly, that C is strictly less than 2 (known to be the best constant in the noncentred case).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 1 , 1998 , pp. 1 - 9
Copyright
Copyright © Royal Society of Edinburgh 1998

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