## Illinois Journal of Mathematics

### Characterizations of various domains of holomorphy via $\bar{\partial}$ estimates and applications to a problem of Kohn

Steven G. Krantz

#### Abstract

It is shown that the only pseudoconvex sets with smooth boundary in $\mathbf{C}^{n}$ on which $\bar{\partial}$ satisfies Lipschitz smoothing estimates of order $1/2$ are the strongly pseudoconvex ones. Various extensions of this result are made to weakly pseudoconvex domains of finite type and in various norms. It is proved that subelliptic estimates for $\bar{\partial}$ can hold on a pseudoconvex set in $\mathbf{C}^{n}$ only if the domain is of finite type in the sense of Kohn.

#### Article information

Source
Illinois J. Math., Volume 23, Issue 2 (1979), 267-285.

Dates
First available in Project Euclid: 20 October 2009

https://projecteuclid.org/euclid.ijm/1256048239

Digital Object Identifier
doi:10.1215/ijm/1256048239

Mathematical Reviews number (MathSciNet)
MR528563

Zentralblatt MATH identifier
0394.32009

Subjects
Primary: 32F15
Secondary: 32F20

#### Citation

Krantz, Steven G. Characterizations of various domains of holomorphy via $\bar{\partial}$ estimates and applications to a problem of Kohn. Illinois J. Math. 23 (1979), no. 2, 267--285. doi:10.1215/ijm/1256048239. https://projecteuclid.org/euclid.ijm/1256048239