no. 1
Distribution function inequalities for the density of the area integral
Annales de l'Institut Fourier, Tome 41 (1991) no. 1, pp. 137-171.

Nous démontrons des “inégalités des bons λ" pour l’intégale d’aire, la fonction maximale non-tangentielle, et la fonction maximale associée à la densité de l’intégrale d’aire. Nos résultats répondent à une question posée par R. F. Gundy. De plus nous démontrons un théorème du genre loi du logarithme itéré pour des fonctions harmoniques, semblable à celui de Kesten pour la suite des sommes partielles de variables indépendantes. Nos théorèmes 1 et 2 sont énoncés pour un domaine dont la frontière est lipschitzienne. Mais, ils sont tout aussi nouveaux pour R + 2 .

We prove good-λ inequalities for the area integral, the nontangential maximal function, and the maximal density of the area integral. This answers a question raised by R. F. Gundy. We also prove a Kesten type law of the iterated logarithm for harmonic functions. Our Theorems 1 and 2 are for Lipschitz domains. However, all our results are new even in the case of R + 2 .

@article{AIF_1991__41_1_137_0,
     author = {Banuelos, R. and Moore, C. N.},
     title = {Distribution function inequalities for the density of the area integral},
     journal = {Annales de l'Institut Fourier},
     pages = {137--171},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {41},
     number = {1},
     year = {1991},
     doi = {10.5802/aif.1252},
     mrnumber = {92k:42025},
     zbl = {0727.42016},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1252/}
}
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Banuelos, R.; Moore, C. N. Distribution function inequalities for the density of the area integral. Annales de l'Institut Fourier, Tome 41 (1991) no. 1, pp. 137-171. doi : 10.5802/aif.1252. http://www.numdam.org/articles/10.5802/aif.1252/

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