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

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 .

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 .

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     title = {Distribution function inequalities for the density of the area integral},
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Banuelos, R.; Moore, C. N. Distribution function inequalities for the density of the area integral. Annales de l'Institut Fourier, Volume 41 (1991) no. 1, pp. 137-171. doi : 10.5802/aif.1252. http://archive.numdam.org/articles/10.5802/aif.1252/

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