Nonnormal Blaschke quotients

Shinji Yamashita
1982 Pacific Journal of Mathematics  
A quotient BJB 2 of two infinite Blaschke products B γ and B 2 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 < oo, there exists a nonnormal Blaschke quotient / such that iί, -\z \Y I f(z) | 2 /(1 + I f(z) \*)*dxdy This might be of interest because, if g is meromorphic in D and if (ί I g f {z) |7tt + I g(z) \ 2 ) 2 dxdy < oo, then g is
more » ... < oo, then g is normal in D.
doi:10.2140/pjm.1982.101.247 fatcat:oechodspn5dl5pzrv6ncyof76q