Sous les hypothèses standard de l’axiomatique Brelot, étude de classes de fonctions harmoniques complexes définies comme les classes de Hardy classiques. Caractérisation comme solutions de problèmes de Dirichlet avec la frontière minimale, les filtres fins, et données-frontière dans , pour , comme intégrales de mesures complexes finies sur la frontière minimale, pour . Existence presque-partout à la frontière minimale d’une limite fine finie . Application à deux théorèmes du type F. et M. Riesz et Phragmen-Lindelöf pour fonctions positives “fortement sous harmoniques”, et à la classification des espaces harmoniques.
@article{AIF_1967__17_2_425_0, author = {Lumer-Na{\"\i}m, Linda}, title = {${\mathcal {H}}^p$-spaces of harmonic functions}, journal = {Annales de l'Institut Fourier}, pages = {425--469}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {17}, number = {2}, year = {1967}, doi = {10.5802/aif.276}, mrnumber = {37 #1642}, zbl = {0153.43102}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.276/} }
TY - JOUR AU - Lumer-Naïm, Linda TI - ${\mathcal {H}}^p$-spaces of harmonic functions JO - Annales de l'Institut Fourier PY - 1967 SP - 425 EP - 469 VL - 17 IS - 2 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/aif.276/ DO - 10.5802/aif.276 LA - en ID - AIF_1967__17_2_425_0 ER -
Lumer-Naïm, Linda. ${\mathcal {H}}^p$-spaces of harmonic functions. Annales de l'Institut Fourier, Volume 17 (1967) no. 2, pp. 425-469. doi : 10.5802/aif.276. http://archive.numdam.org/articles/10.5802/aif.276/
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