Blaschke products and nonideal ideals in higher order Lipschitz algebras

Abstract

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 $H_n^{\infty }=\{f:f^{(n)}\in H^{\infty }\}$ rather than for its more manageable Zygmund-type version. This part is based on a new theorem concerning the canonical factorization in $H_n^{\infty }$.

arXiv comment17 pages