Extension of CR functions to «wedge type» domains

D'Agnolo, Andrea, D'Ancona, Piero, and Zampieri, Giuseppe. "Extension of CR functions to «wedge type» domains." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 2.1 (1991): 35-42. <http://eudml.org/doc/244287>.

@article{DAgnolo1991,
abstract = {Let \( X \) be a complex manifold, \( S \) a generic submanifold of \( X^\{\mathbb\{R\}\} \), the real underlying manifold to \( X \). Let \( \Omega \) be an open subset of \( S \) with \( \partial \Omega \) analytic, \( Y \) a complexification of \( S \). We first recall the notion of \( \Omega \)-tuboid of \( X \) and of \( Y \) and then give a relation between; we then give the corresponding result in terms of microfunctions at the boundary. We relate the regularity at the boundary for \( \bar\{\partial\}\_\{b\} \) to the extendability of \( CR \) functions on \( \Omega \) to \( \Omega \)-tuboids of \( X \). Next, if \( X \) has complex dimension 2, we give results on extension for some classes of hypersurfaces (which correspond to some \( \bar\{\partial\}\_\{b\} \) whose Poisson bracket between real and imaginary part is \( \ge 0 \)). The main tools of the proof are the complex \( \mathcal\{C\}\_\{\Omega \mid Y\} \) by Schapira and the theorem of \( \Omega \)-regularity of Schapira-Zampieri and Uchida-Zampieri.},
author = {D'Agnolo, Andrea, D'Ancona, Piero, Zampieri, Giuseppe},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Partial differential equations on manifolds; Several complex variables and analytic spaces; Boundary value problems; regularity at the boundary; extendability of -functions; hyperfunctions},
language = {eng},
month = {3},
number = {1},
pages = {35-42},
publisher = {Accademia Nazionale dei Lincei},
title = {Extension of CR functions to «wedge type» domains},
url = {http://eudml.org/doc/244287},
volume = {2},
year = {1991},
}

TY - JOUR
AU - D'Agnolo, Andrea
AU - D'Ancona, Piero
AU - Zampieri, Giuseppe
TI - Extension of CR functions to «wedge type» domains
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1991/3//
PB - Accademia Nazionale dei Lincei
VL - 2
IS - 1
SP - 35
EP - 42
AB - Let \( X \) be a complex manifold, \( S \) a generic submanifold of \( X^{\mathbb{R}} \), the real underlying manifold to \( X \). Let \( \Omega \) be an open subset of \( S \) with \( \partial \Omega \) analytic, \( Y \) a complexification of \( S \). We first recall the notion of \( \Omega \)-tuboid of \( X \) and of \( Y \) and then give a relation between; we then give the corresponding result in terms of microfunctions at the boundary. We relate the regularity at the boundary for \( \bar{\partial}_{b} \) to the extendability of \( CR \) functions on \( \Omega \) to \( \Omega \)-tuboids of \( X \). Next, if \( X \) has complex dimension 2, we give results on extension for some classes of hypersurfaces (which correspond to some \( \bar{\partial}_{b} \) whose Poisson bracket between real and imaginary part is \( \ge 0 \)). The main tools of the proof are the complex \( \mathcal{C}_{\Omega \mid Y} \) by Schapira and the theorem of \( \Omega \)-regularity of Schapira-Zampieri and Uchida-Zampieri.
LA - eng
KW - Partial differential equations on manifolds; Several complex variables and analytic spaces; Boundary value problems; regularity at the boundary; extendability of -functions; hyperfunctions
UR - http://eudml.org/doc/244287
ER -