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The corona theorem on the complement of certain square cantor sets

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Abstract

Let K be a square Cantor set, i.e., the Cartesian product K = E × E of two linear Cantor sets. Let δ n denote the proportion of the intervals removed in the nth stage of the construction of E. It is shown that if \( \delta _n = o(\frac{1} {{\log \log n}}) \), then the corona theorem holds on the domain Ω = ℂ* \ K.

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  1. Department of Mathematics, University of california, Los Angeles, CA, 90095-1555, USA

    Jon Handy

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Handy, J. The corona theorem on the complement of certain square cantor sets. J Anal Math 108, 1–18 (2009). https://doi.org/10.1007/s11854-009-0016-1

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  • DOI: https://doi.org/10.1007/s11854-009-0016-1

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