A limiting weak type estimate for capacitary maximal function

Jie Xiao; Ning Zhang

doi:10.1016/j.crma.2013.11.008

Potential theory/Harmonic analysis

A limiting weak type estimate for capacitary maximal function

Presented by: Jean-Michel Bony

Jie Xiao ¹; Ning Zhang ¹

¹Department of Mathematics and Statistics, Memorial University, St. Johnʼs, NL A1C 5S7, Canada

Comptes Rendus. Mathématique, Volume 352 (2014) no. 1, pp. 7-11

is referenced by Corrigendum to “A limiting weak type estimate for capacitary maximal function” [C. R. Acad. Sci. Paris, Ser. I 352 (1) (2014) 7–11]

Abstract (Original language)
Résumé

A capacitary analogue of the limiting weak type estimate of P. Janakiraman for the Hardy–Littlewood maximal function of an $L^{1} (R^{n})$ -function (cf. [5,6]) is discovered.

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.

Received: 2013-07-30
Accepted: 2013-11-13
Published online: 2013-12-19

DOI: 10.1016/j.crma.2013.11.008

Author's affiliations:

Jie Xiao ¹ ; Ning Zhang ¹

¹ Department of Mathematics and Statistics, Memorial University, St. Johnʼs, NL A1C 5S7, Canada

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Jie Xiao; Ning Zhang. A limiting weak type estimate for capacitary maximal function. Comptes Rendus. Mathématique, Volume 352 (2014) no. 1, pp. 7-11. doi: 10.1016/j.crma.2013.11.008

References
Cited by

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

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

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Cited by Sources:

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

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