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A counter-example for the Bezout equation in the Hardy classH p

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Abstract

Leff 1,f 2 be bounded holomorphic functions in the unit disc\(\mathbb{D}\) of the complex plane ℂ. Using a recent result of S. Treil about estimates in the corona theorem, we strengthen a counterexample given by Amar, Bruna and Nicolau to the existence of functionsg 1,g 2 in the Hardy spaceH p (\(\mathbb{D}\)) verifying the Bezout equationf 1 g 1+f 2 g 2=1.

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References

  1. E. Amar, J. Bruna and A. Nicolau,On H p -solutions of the Bezout equation, Pacific J. Math171 (1995), 297–307.

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Authors and Affiliations

  1. Laboratoire LaBAG UFR Mathématiques/Informatique, Université Bordeaux I, 351, cours de la Libération, F-33405, Talence/Cedex, France

    E. Amar

  2. Department de Matemàtiques, Universita Autònoma de Barcelona, 08193, Bellaterra (Barcelona), Spain

    N. Marco

Authors
  1. E. Amar
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  2. N. Marco
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Correspondence to E. Amar.

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Amar, E., Marco, N. A counter-example for the Bezout equation in the Hardy classH p . J. Anal. Math. 95, 121–131 (2005). https://doi.org/10.1007/BF02791499

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  • DOI: https://doi.org/10.1007/BF02791499

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