Complex tangential characterizations of Hardy-Sobolev Spaces of holomorphic functions.
- Autores: Sandrine Grellier
- Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 9, Nº 2, 1993, págs. 201-255
- Idioma: inglés
- DOI: 10.4171/rmi/135
- Títulos paralelos:
- Caracterizaciones tangenciales complejas de espacios Hardy-Sobolev de funciones holomorfas
- Enlaces
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Resumen
Let O be a C8-domain in Cn. It is well known that a holomorphic function on O behaves twice as well in complex tangential directions (see [GS] and [Kr] for instance). It follows from well known results (see [H], [RS]) that some converse is true for any kind of regular functions when O satisfies (P) The real tangent space is generated by the Lie brackets of real and imaginary parts of complex tangent vectors In this paper we are interested in the behavior of holomorphic Hardy-Sobolev functions in complex tangential directions. Our aim is to give a characterization of these spaces, defined in a domain which satisfies the property (P), involving only complex tangential derivatives. Our method, which is elementary, is to prove pointwise estimates between gradients and tangential gradients of holomorphic functions and, next, to use them to obtain the characterization of Hardy-Sobolev spaces for 1 = p < 8.
