Vol. 101, No. 1, 1982

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Nonnormal Blaschke quotients

Shinji Yamashita

Vol. 101 (1982), No. 1, 247–254
Abstract

A quotient B1∕B2 of two infinite Blaschke products B1 and B2 with no common zero is called a Blaschke quotient. The existence of a Blaschke quotient which is not normal in the open unit disk D, is well known. We shall show among other things, that, for each p, 0 < p < , there exists a nonnormal Blaschke quotient f such that

∫ ∫
(1− |z|)p|f ′(z)|2∕(1+ |f (z)|2)2dx dy < ∞.
D

This might be of interest because, if g is meromorphic in D and if D|g(z)|2(1 + |g(z)|2)2 dxdy < , then g is normal in D.

Mathematical Subject Classification 2000
Primary: 30D45
Secondary: 30D50
Milestones
Received: 6 April 1979
Published: 1 July 1982
Authors
Shinji Yamashita