Blaschke products and nonideal ideals in higher order Lipschitz algebras

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 $H^\infty_n$.