Título inglés |
Growth and asymptotic sets of subharmonic functions (II) |
Título español |
Crecimiento y conjuntos asintóticos de funciones subarmónicas (II). |
Autor/es |
Wu, Jang-Mei |
Organización |
Dep. Math. Univ. Illinois, Urbana (Illinois), Estados Unidos |
Revista |
0214-1493 |
Publicación |
1998, 42 (2): 449-460, 7 Ref. |
Tipo de documento |
articulo |
Idioma |
Inglés |
Resumen inglés |
We study the relation between the growth of a subharmonic function
in the half space Rn+1+ 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 Rn+1+ satisfying the growth condition of order α : u(x) ≤ x-αn+1 for 0 < xn+1 < 1, such that the
Hausdorff dimension of the asymptotic set Èλ≠0A(λ) is exactly
n-α. Here A(λ) is the set of boundary points at which f tends to
λ along some curve. This proves the sharpness of a theorem due to Berman, Barth, Rippon, Sons, Fernández, Heinonen, Llorente and Gardiner cumulatively. |
Clasificación UNESCO |
120224 |
Palabras clave español |
Función subarmónica ; Comportamiento asintótico ; Factores de crecimiento |
Código MathReviews |
MR1677612 |
Acceso al artículo completo |