Nonnormal Dirichlet quotients and nonnormal Blaschke quotients

Yamashita, Shinji

doi:10.1090/S0002-9939-1980-0587936-3

Nonnormal Dirichlet quotients and nonnormal Blaschke quotients
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by Shinji Yamashita

Proc. Amer. Math. Soc. 80 (1980), 604-606

DOI: https://doi.org/10.1090/S0002-9939-1980-0587936-3

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Abstract:

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

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