no. 1
Potential theory/Harmonic analysis
A limiting weak type estimate for capacitary maximal function
[Une estimation de type faible limite pour la fonction maximale capacitaire]

Présenté par : Jean-Michel Bony

Xiao, Jie1 ; Zhang, Ning1
1 Department of Mathematics and Statistics, Memorial University, St. Johnʼs, NL A1C 5S7, Canada
Comptes Rendus. Mathématique, Tome 352 (2014) no. 1, pp. 7-11.

Pour lʼanalogue en termes de capacités de la fonction maximale de Hardy–Littlewood, on démontre une estimation de type faible limite correspondant à celle de P. Janakiraman.

A capacitary analogue of the limiting weak type estimate of P. Janakiraman for the Hardy–Littlewood maximal function of an L1(Rn)-function (cf. [5,6]) is discovered.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.11.008
Xiao, Jie 1 ; Zhang, Ning 1

1 Department of Mathematics and Statistics, Memorial University, St. Johnʼs, NL A1C 5S7, Canada 
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Xiao, Jie; Zhang, Ning. A limiting weak type estimate for capacitary maximal function. Comptes Rendus. Mathématique, Tome 352 (2014) no. 1, pp. 7-11. doi : 10.1016/j.crma.2013.11.008. http://www.numdam.org/articles/10.1016/j.crma.2013.11.008/

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[4] Brown, R. Lecture notes: harmonic analysis http://www.ms.uky.edu/~rbrown/courses/ma773/notes.pdf

[5] Janakiraman, P. Limiting weak-type behavior for singular integral and maximal operators, Trans. Amer. Math. Soc., Volume 358 (2006), pp. 1937-1952

[6] Janakiraman, P. Limiting weak-type behavior for the Riesz transform and maximal operator when λ→∞, Michigan Math. J., Volume 55 (2007), pp. 35-50

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☆ Project supported by NSERC of Canada as well as by URP of Memorial University, Canada.