Complex tangential characterizations of Hardy-Sobolev spaces of holomorphic functions.

Grellier, Sandrine. "Complex tangential characterizations of Hardy-Sobolev spaces of holomorphic functions.." Revista Matemática Iberoamericana 9.2 (1993): 201-255. <http://eudml.org/doc/39436>.

@article{Grellier1993,
abstract = {Let Ω be a C∞-domain in Cn. It is well known that a holomorphic function on Ω 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 Ω satisfies(P)    The real tangent space is generated by the Lie brackets of real and imaginary parts of complex tangent vectorsIn 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 &lt; ∞.},
author = {Grellier, Sandrine},
journal = {Revista Matemática Iberoamericana},
keywords = {Espacios de Sobolev; Funciones holomorfas; Desigualdades; Funciones pseudoconvexas; Normativa; tangent space; complex tangential derivatives; mean value operator; maximal admissible function; Hardy-Sobolev spaces},
language = {eng},
number = {2},
pages = {201-255},
title = {Complex tangential characterizations of Hardy-Sobolev spaces of holomorphic functions.},
url = {http://eudml.org/doc/39436},
volume = {9},
year = {1993},
}

TY - JOUR
AU - Grellier, Sandrine
TI - Complex tangential characterizations of Hardy-Sobolev spaces of holomorphic functions.
JO - Revista Matemática Iberoamericana
PY - 1993
VL - 9
IS - 2
SP - 201
EP - 255
AB - Let Ω be a C∞-domain in Cn. It is well known that a holomorphic function on Ω 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 Ω satisfies(P)    The real tangent space is generated by the Lie brackets of real and imaginary parts of complex tangent vectorsIn 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 &lt; ∞.
LA - eng
KW - Espacios de Sobolev; Funciones holomorfas; Desigualdades; Funciones pseudoconvexas; Normativa; tangent space; complex tangential derivatives; mean value operator; maximal admissible function; Hardy-Sobolev spaces
UR - http://eudml.org/doc/39436
ER -