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Remark on “Maximal
functions on the unit n-sphere”
by Peter M. Knopf (1987)
Hong-Quan Li |
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Vol. 263 (2013), No. 1, 253–256
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Correction to Pacific Journal of Mathematics 129 (1987) 77–84 |
Abstract |
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The article in question contains an important result on the behavior of the Hardy–Littlewood maximal function MSn on the unit n-sphere, providing a weak-type linear bound that has not been improved on in the intervening decades. Unfortunately, the proof has a gap, since it relies on an incorrect intermediate result (Lemma 3). We correct the proof by providing a sharper lower bound for a trigonometry integral than the one used by Knopf. |
Keywords
Hardy–Littlewood maximal function, sphere
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Mathematical Subject Classification 2010
Primary: 42B25, 43A85
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Milestones
Received: 3 April 2012
Revised: 6 September 2012
Accepted: 22 October 2012
Published: 14 May 2013
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Authors |
| Hong-Quan Li | |
| School of Mathematical
Sciences Fudan University 220 Handan Road Shanghai 200433 China |
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