Geodesic
Mean Growth of Harmonic Functions of Beurling Type
Canadian mathematical bulletin, Tome 27 (1984) no. 4, pp. 405-409

Voir la notice de l'article provenant de la source Cambridge University Press

A harmonic function on the unit disc is of Beurling type ω if its Fourier (or Taylor) coefficients grow no faster than exp ω(|n|) as |n|→∞, where ω is a given increasing, concave function with ω(x)/x ↓ 0 as x → ∞. These harmonic functions are characterized by the growth rate of their L 1-norms on circles of radius r as r → 1. The classical Schwartz result follows as a corollary by taking ω(x) = log(1+x). The Gevrey case is also included in the general result if one uses ω(x) = x α, 0 < α < 1.
DOI : 10.4153/CMB-1984-062-0
Mots-clés : 31A05, 31A25, 46F05 
Collier, Manning G.; Kelingos, John A. Mean Growth of Harmonic Functions of Beurling Type. Canadian mathematical bulletin, Tome 27 (1984) no. 4, pp. 405-409. doi: 10.4153/CMB-1984-062-0
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