, Volume 86, Issue 1, pp 139-182

The majorization function and the index of invariant sub spaces in the Bergman spaces

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Abstract

The index of an invariant subspace ℳ of a Banach space of analytic functions in the open unit disc is defined by ind = dimℳ/zℳ. In this paper, we provide a strong link between high index and nontangential boundary behaviour of the functions in an invariant subspace.

Work of the first author was partially supported by the Royal Swedish Academy of Sciences; work of the second and third authors was supported by the National Science Foundation.