Comptes Rendus
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

Jie Xiao1 ; Ning Zhang1
1 Department of Mathematics and Statistics, Memorial University, St. Johnʼs, NL A1C 5S7, Canada
Comptes Rendus. Mathématique, Volume 352 (2014) no. 1, pp. 7-11.
est référencé par Corrigendum to “A limiting weak type estimate for capacitary maximal function” [C. R. Acad. Sci. Paris, Ser. I 352 (1) (2014) 7–11]

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.11.008

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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.11.008/

[1] D.R. Adams A note on Choquet integrals with respect to Hausdorff capacity, Lecture Notes in Mathematics, vol. 1302, Springer, 1988, pp. 115-124

[2] D.R. Adams Choquet integrals in potential theory, Publ. Mat., Volume 42 (1998), pp. 3-66

[3] I. Asekritova; J. Cerda; N. Kruglyak The Riesz–Herz equivalence for capacity maximal functions, Rev. Mat. Complut., Volume 25 (2012), pp. 43-59

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

[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→∞, Michigan Math. J., Volume 55 (2007), pp. 35-50

[7] J. Kinnunen The Hardy–Littlewood maximal function of a Sobolev function, Israel J. Math., Volume 100 (1997), pp. 117-224

[8] N. Kruglyak; E.A. Kuznetsov Sharp integral estimates for the fractional maximal function and interpolation, Ark. Mat., Volume 44 (2006), pp. 309-326

[9] J. Xiao Carleson embeddings for Sobelev spaces via heat equation, J. Differential Equations, Volume 224 (2006), pp. 277-295

  • Hanli Tang; Guanglan Wang Limiting weak type behavior for multilinear fractional integrals, Nonlinear Analysis, Volume 197 (2020), p. 111858 | DOI:10.1016/j.na.2020.111858

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

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