Blaschke products and nonideal ideals in higher order Lipschitz algebras

Dyakonov, K.

doi:10.1090/S1061-0022-2010-01127-0

Blaschke products and nonideal ideals in higher order Lipschitz algebras
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by K. M. Dyakonov

St. Petersburg Math. J. 21 (2010), 979-993

DOI: https://doi.org/10.1090/S1061-0022-2010-01127-0

Published electronically: September 22, 2010

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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 $H^\infty _n=\{f : f^{(n)}\in H^\infty \}$ 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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