We prove good- 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 .
Nous démontrons des “inégalités des bons " 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 .
@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/} }
TY - JOUR AU - Banuelos, R. AU - Moore, C. N. TI - Distribution function inequalities for the density of the area integral JO - Annales de l'Institut Fourier PY - 1991 SP - 137 EP - 171 VL - 41 IS - 1 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.1252/ DO - 10.5802/aif.1252 LA - en ID - AIF_1991__41_1_137_0 ER -
%0 Journal Article %A Banuelos, R. %A Moore, C. N. %T Distribution function inequalities for the density of the area integral %J Annales de l'Institut Fourier %D 1991 %P 137-171 %V 41 %N 1 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/aif.1252/ %R 10.5802/aif.1252 %G en %F AIF_1991__41_1_137_0
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://www.numdam.org/articles/10.5802/aif.1252/
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