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- W2329907903 abstract "Abstract 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." @default.
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- W2329907903 date "1984-12-01" @default.
- W2329907903 modified "2023-10-14" @default.
- W2329907903 title "Mean Growth of Harmonic Functions of Beurling Type" @default.
- W2329907903 doi "https://doi.org/10.4153/cmb-1984-062-0" @default.
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