## Tsukuba Journal of Mathematics

### Cauchy-Riemann orbifolds

#### Abstract

For any $CR$ orbifold $B$, of $CR$ dimension $n$, we build a vector bundle (in the sense of J. Girbau & M. Nicolau, [13]) $T_{1,0}(B)$ over $B$, so that $T_{1,0}(B)_{p} \approx \bm{C}^{n}/G_{x}$ at any singular point $p=\varphi(x)\in B$ (and the portion of $T_{1,0}(B)$ over the regular part of $B$ is an ordinary $CR$ stmcture), hence study the tangential Cauchy--Riemann equations on orbifolds. As an application, we build a two-sided parametrix for for the Kohn--Rossi laplacian $\Box_{\Omega}$ (on the domain $\Omega$ of a local uniformizing system $\{\Omega, G, \varphi\}$ of $B$) inverting $\Box_{\Omega}$ over the $G$-invariant $(0, q)$-forms $(1 \leq q \leq n-1)$ up to (smoothing) operators of type $1$ (in the sense of G. B. Folland & E. M. Stein, [12]).

#### Article information

Source
Tsukuba J. Math., Volume 26, Number 2 (2002), 351-386.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496164430

Digital Object Identifier
doi:10.21099/tkbjm/1496164430

Mathematical Reviews number (MathSciNet)
MR1940400

Zentralblatt MATH identifier
1023.32021

#### Citation

Dragomir, Sorin; Masamune, Jun. Cauchy-Riemann orbifolds. Tsukuba J. Math. 26 (2002), no. 2, 351--386. doi:10.21099/tkbjm/1496164430. https://projecteuclid.org/euclid.tkbjm/1496164430