# Growth and asymptotic sets of subharmonic functions (II)

Publicacions Matemàtiques (1998)

- Volume: 42, Issue: 2, page 449-460
- ISSN: 0214-1493

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topWu, Jang-Mei. "Growth and asymptotic sets of subharmonic functions (II)." Publicacions Matemàtiques 42.2 (1998): 449-460. <http://eudml.org/doc/41344>.

@article{Wu1998,

abstract = {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 ∪λ≠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.},

author = {Wu, Jang-Mei},

journal = {Publicacions Matemàtiques},

keywords = {Función subarmónica; Comportamiento asintótico; Factores de crecimiento; asymptotic values; subharmonic function; boundary points; Hausdorff dimension},

language = {eng},

number = {2},

pages = {449-460},

title = {Growth and asymptotic sets of subharmonic functions (II)},

url = {http://eudml.org/doc/41344},

volume = {42},

year = {1998},

}

TY - JOUR

AU - Wu, Jang-Mei

TI - Growth and asymptotic sets of subharmonic functions (II)

JO - Publicacions Matemàtiques

PY - 1998

VL - 42

IS - 2

SP - 449

EP - 460

AB - 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 ∪λ≠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.

LA - eng

KW - Función subarmónica; Comportamiento asintótico; Factores de crecimiento; asymptotic values; subharmonic function; boundary points; Hausdorff dimension

UR - http://eudml.org/doc/41344

ER -

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