Growth and asymptotic sets of subharmonic functions (II)
Jang-Mei Wu (1998)
Publicacions Matemàtiques
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We study the relation between the growth of a subharmonic function in the half space R and the size of its asymptotic set. In particular, we prove that for any n ≥ 1 and 0 < α ≤ n, there exists a subharmonic function u in the R satisfying the growth condition of order α : u(x) ≤ x for 0 < x < 1, such that the Hausdorff dimension of the asymptotic set ∪A(λ) is exactly n-α. Here A(λ) is the set of boundary points at which...