Blaschke products and nonideal ideals in higher order Lipschitz algebras

Details Blaschke products and nonideal ideals in higher order Lipschitz algebras Blaschke products and nonideal ideals in higher order Lipschitz algebras

2010-04-09

arxiv.org/abs/1004.1444v1

Algebra i Analiz, Vol. 21 (2009), No. 6, 182--201

Mathematics

Complex Variables

17 pages

Scientific paper

We investigate certain ideals (associated with Blaschke products) of the analytic Lipschitz algebra $A^\alpha$, with $\alpha>1$, that fail to be "ideal spaces". The latter means that the ideals in question are not describable by any size condition on the function's modulus. In the case where $\alpha=n$ is an integer, we study this phenomenon for the algebra $H^\infty_n=\{f:f^{(n)}\in H^\infty\}$ rather than for its more manageable Zygmund-type version. This part is based on a new theorem concerning the canonical factorization in $H^\infty_n$.

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