Uniform estimates for the Cauchy-Riemann equation on $q$-convex wedges

Laurent-Thiébaut, Christine, and Leiterer, Jurgen. "Uniform estimates for the Cauchy-Riemann equation on $q$-convex wedges." Annales de l'institut Fourier 43.2 (1993): 383-436. <http://eudml.org/doc/75002>.

@article{Laurent1993,
abstract = {We study the $\overline\{\partial \}$-equation with Hölder estimates in $q$-convex wedges of $\{\Bbb C\}^n$ by means of integral formulas. If $D \subset \{\Bbb C\}^ n$ is defined by some inequalities $\lbrace \rho _i \le 0\rbrace $, where the real hypersurfaces $\lbrace \rho _i=0\rbrace $ are transversal and any nonzero linear combination with nonnegative coefficients of the Levi form of the $\rho _ i$’s have at least $(q+1)$ positive eigenvalues, we solve the equation $\overline\{\partial \}f=g$ for each continuous $(n,r)$-closed form $g$ in $D$, $n-q \le r \le n$, with the following estimates: if $d$ denotes the distance to the boundary of $D$ and if $d^\beta g$ is bounded, then for all $\varepsilon &gt;0$, $f$ is Hölder continuous with exponent $1/2-\beta -\varepsilon $ if $0 \le \beta &lt; 1/2$ and $d^\{\beta +\varepsilon -1/2\}f$ is bounded if $1/2 \le \beta &lt; 1$.},
author = {Laurent-Thiébaut, Christine, Leiterer, Jurgen},
journal = {Annales de l'institut Fourier},
keywords = {integral formula with uniform estimates; piecewise smooth -convex domains; tangential Cauchy-Riemann equations},
language = {eng},
number = {2},
pages = {383-436},
publisher = {Association des Annales de l'Institut Fourier},
title = {Uniform estimates for the Cauchy-Riemann equation on $q$-convex wedges},
url = {http://eudml.org/doc/75002},
volume = {43},
year = {1993},
}

TY - JOUR
AU - Laurent-Thiébaut, Christine
AU - Leiterer, Jurgen
TI - Uniform estimates for the Cauchy-Riemann equation on $q$-convex wedges
JO - Annales de l'institut Fourier
PY - 1993
PB - Association des Annales de l'Institut Fourier
VL - 43
IS - 2
SP - 383
EP - 436
AB - We study the $\overline{\partial }$-equation with Hölder estimates in $q$-convex wedges of ${\Bbb C}^n$ by means of integral formulas. If $D \subset {\Bbb C}^ n$ is defined by some inequalities $\lbrace \rho _i \le 0\rbrace $, where the real hypersurfaces $\lbrace \rho _i=0\rbrace $ are transversal and any nonzero linear combination with nonnegative coefficients of the Levi form of the $\rho _ i$’s have at least $(q+1)$ positive eigenvalues, we solve the equation $\overline{\partial }f=g$ for each continuous $(n,r)$-closed form $g$ in $D$, $n-q \le r \le n$, with the following estimates: if $d$ denotes the distance to the boundary of $D$ and if $d^\beta g$ is bounded, then for all $\varepsilon &gt;0$, $f$ is Hölder continuous with exponent $1/2-\beta -\varepsilon $ if $0 \le \beta &lt; 1/2$ and $d^{\beta +\varepsilon -1/2}f$ is bounded if $1/2 \le \beta &lt; 1$.
LA - eng
KW - integral formula with uniform estimates; piecewise smooth -convex domains; tangential Cauchy-Riemann equations
UR - http://eudml.org/doc/75002
ER -