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A note on the one-dimensional maximal function*

Published online by Cambridge University Press:  14 November 2011

Antonio Bernal
Antonio Bernal
Affiliation:
Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, 08071 Barcelona, Spain
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Synopsis

In this note, we consider the Hardy-Littlewood maximal function on R for arbitrary measures, as was done by Peter Sjögren in a previous paper. We determine the best constant for the weak type inequality.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 111 , Issue 3-4 , 1989 , pp. 325 - 328
Copyright
Copyright © Royal Society of Edinburgh 1989

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References

1Guzman, M. de. Differentiation of integrals in ℝn, Lecture Notes in Mathematics 481 (Berlin: Springer, 1975).Google Scholar
2Sjögren, P.. A remark on the maximal function for measures in ℝn. Amer. J. Math. 105 (1983), 1231–1233.CrossRefGoogle Scholar