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A Vector-valued Hp Corona Theorem on the Polydisk

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Abstract.

For the corona problem on the bidisk, we find analytic solutions belonging to the Orlicz-type space \(\exp {\left( {L^{{\frac{1}{3}}} } \right)}.\) In addition, for 1  ≤   p  <  ∞, an \( \mathcal{H}^{p} {\left( {D^{2} } \right)}\) corona theorem is established. Similar techniques can be used for the polydisk.

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Authors and Affiliations

  1. Department of Mathematics, The University of Alabama, P.O. Box 870350, Tuscaloosa, AL, 35487-0350, USA

    Tavan T. Trent

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  1. Tavan T. Trent
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Correspondence to Tavan T. Trent.

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Trent, T.T. A Vector-valued Hp Corona Theorem on the Polydisk. Integr. equ. oper. theory 56, 129–149 (2006). https://doi.org/10.1007/s00020-005-1406-0

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  • DOI: https://doi.org/10.1007/s00020-005-1406-0

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