A reverse Denjoy theorem II
Tóm tắt
For α satisfying 0 < α < π, suppose that C
1 and C
2 are rays from the origin, C
1: z = re
i(π−α) and C
2: z = re
i(π+α), r ≥ 0, and that D = {z: | arg z − π| < α}. Let u be a nonconstant subharmonic function in the plane and define B(r, u) = sup|z|=r
u(z) and A
D
(r, u) =
$$
\inf _{z \in \bar D_r }
$$
u(z), where D
r
= {z: z ∈ D and |z| = r}. If u(z) = (1 + o(1))B(|z|, u) as z → ∞ on C
1 ∪ C
2 and A
D
(r, u) = o(B(r, u)) as r → ∞, then the lower order of u is at least π/(2α).
Tài liệu tham khảo
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