On the centered Hardy-Littlewood maximal operator
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- by Antonios D. Melas
- Trans. Amer. Math. Soc. 354 (2002), 3263-3273
- DOI: https://doi.org/10.1090/S0002-9947-02-02900-8
- Published electronically: February 20, 2002
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Abstract:
We will study the centered Hardy-Littlewood maximal operator acting on positive linear combinations of Dirac deltas. We will use this to obtain improvements in both the lower and upper bounds or the best constant $C$ in the $L^{1}\rightarrow$ weak $L^{1}$ inequality for this operator. In fact we will show that $\frac {11+\sqrt {61}}{12}=1.5675208...\leq C\leq \frac {5} {3}=1.66...$.References
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Bibliographic Information
- Antonios D. Melas
- Affiliation: Department of Mathematics, University of Athens, Panepistimiopolis 15784, Athens, Greece
- MR Author ID: 311078
- Email: amelas@math.uoa.gr
- Received by editor(s): March 14, 2000
- Received by editor(s) in revised form: June 15, 2001
- Published electronically: February 20, 2002
- © Copyright 2002 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 354 (2002), 3263-3273
- MSC (2000): Primary 42B25
- DOI: https://doi.org/10.1090/S0002-9947-02-02900-8
- MathSciNet review: 1897399