1Departamento de Matemática Aplicada and IMPA-UPV ETS Arquitectura Universidad Politécnica de Valencia E-46071 Valencia, Spain 2FB IV – Mathematik Universität Trier D-54286 Trier, Germany 3Departamento de Matemática Aplicada and IMPA-UPV E. Politécnica Superior de Alcoy Universidad Politécnica de Valencia Plaza Ferrándiz y Carbonell 2 E-03801 Alcoy (Alicante), Spain
Studia Mathematica, Tome 183 (2007) no. 3, pp. 225-248
We present a unified approach to the study of extensions of vector-valued holomorphic or harmonic functions based on the existence of weak or weak$^*$-holomorphic or harmonic extensions. Several recent results due to Arendt, Nikolski, Bierstedt, Holtmanns and Grosse-Erdmann are extended. An open problem by Grosse-Erdmann is solved in the negative. Using the extension results we prove existence of Wolff type representations for the duals of certain function spaces.
Keywords:
present unified approach study extensions vector valued holomorphic harmonic functions based existence weak weak * holomorphic harmonic extensions several recent results due arendt nikolski bierstedt holtmanns grosse erdmann extended problem grosse erdmann solved negative using extension results prove existence wolff type representations duals certain function spaces
1
Departamento de Matemática Aplicada and IMPA-UPV ETS Arquitectura Universidad Politécnica de Valencia E-46071 Valencia, Spain
2
FB IV – Mathematik Universität Trier D-54286 Trier, Germany
3
Departamento de Matemática Aplicada and IMPA-UPV E. Politécnica Superior de Alcoy Universidad Politécnica de Valencia Plaza Ferrándiz y Carbonell 2 E-03801 Alcoy (Alicante), Spain
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José Bonet; Leonhard Frerick; Enrique Jordá. Extension of vector-valued holomorphic
and harmonic functions. Studia Mathematica, Tome 183 (2007) no. 3, pp. 225-248. doi: 10.4064/sm183-3-2
