Approximation par fonctions holomorphes dans les espaces Lp, Lip α et BMO
Boivin, André (University of Western Ontario. Department of Mathematics)
Verdera, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	1991
Abstract:	Vitushkin-type theorems on the approximation by holomorphic functions in the complex plane are established. More precisely, let F be a closed (or measurable) subset of the complex plane and let B be any one of the following spaces of functions defined on F:Lp(F), 1 < p <∞, Lipα(F), 0 <α <1, BMO(F), or Cm(F). Let AB be the set of those functions in B which are holomorphic on the interior of F. We characterize, in terms of appropriate capacities, those sets F for which every function in AB can be approximated, in the B-norm on F, by functions holomorphic in a neighbourhood of F. Our argument is along the lines of the original approximation scheme of A. G. Vitushkin and generalizes, to unbounded sets F, results of many authors, including T. Bagby, P. Lindberg, A. G. O'Farrell and J. Verdera. It should be noted that similar results for the uniform norm have been known for some time.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; Versió publicada
Published in:	Indiana University mathematics journal, Vol. 40, No. 2 (1991) , p. 393-418, ISSN 0022-2518

DOI: 10.1512/iumj.1991.40.40021

26 p, 1.5 MB

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