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

Blaschke products and nonideal ideals in higher order Lipschitz algebras