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

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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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     title = {Mean {Growth} of {Harmonic} {Functions} of {Beurling} {Type}},
     journal = {Canadian mathematical bulletin},
     pages = {405--409},
     year = {1984},
     volume = {27},
     number = {4},
     doi = {10.4153/CMB-1984-062-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-062-0/}
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