Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 767-772

A NEW APPROACH TO THE CORONA THEOREM FOR DOMAINS BOUNDED BY A C^1+α CURVE

José Manuel Enriquez-Salamanca and Maria José González

University of Cádiz, Department of Mathematics
Cádiz, 11002, Spain; enrique.desalamanca 'at' uca.es

University of Cádiz, Department of Mathematics
Puerto Real, 11510, Spain; majose.gonzalez 'at' uca.es

Abstract. We prove the corona theorem for domains whose boundary lies in a C^1+α curve. For that, we transfer H^∞ on the complement of the curve onto a Denjoy domain and use the results from Garnett and Jones.

2010 Mathematics Subject Classification: Primary 30H80.

Key words: Cauchy integral, quasiconformal mapping, Carleson measure, smooth curve, corona theorem.

Reference to this article: J.M. Enriquez-Salamanca and M.J. González: A new approach to the corona theorem for domains bounded by a C^1+α curve. Ann. Acad. Sci. Fenn. Math. 40 (2015), 767-772.

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doi:10.5186/aasfm.2015.4043

A NEW APPROACH TO THE CORONA THEOREM FOR DOMAINS BOUNDED BY A C1+α CURVE

José Manuel Enriquez-Salamanca and Maria José González

A NEW APPROACH TO THE CORONA THEOREM FOR DOMAINS BOUNDED BY A C^1+α CURVE