Abstract
There exists a nonnormal meromorphic function f 1 / f 2 {f_1}/{f_2} in U = { | z | > 1 } U = \{ |z| > 1\} , where f 1 {f_1} and f 2 {f_2} both are holomorphic functions with finite Dirichlet integrals in U. For each 0 > α > 1 0 > \alpha > 1 , there exists a nonnormal meromorphic function B 1 / B 2 {B_1}/{B_2} in U, where B 1 {B_1} and B 2 {B_2} both are Blaschke products with finite α \alpha -weighted Dirichlet integrals in U.
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