Characterizations of various domains of holomorphy via $\bar{\partial}$ estimates and applications to a problem of Kohn
Krantz, Steven G.
Illinois J. Math., Tome 23 (1979) no. 4, p. 267-285 / Harvested from Project Euclid
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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.
Publié le : 1979-06-15
Classification:  32F15,  32F20 
@article{1256048239,
     author = {Krantz, Steven G.},
     title = {Characterizations of various domains of holomorphy via $\bar{\partial}$ estimates and applications to a problem of Kohn},
     journal = {Illinois J. Math.},
     volume = {23},
     number = {4},
     year = {1979},
     pages = { 267-285},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1256048239}
}

Krantz, Steven G. Characterizations of various domains of holomorphy via $\bar{\partial}$ estimates and applications to a problem of Kohn. Illinois J. Math., Tome 23 (1979) no. 4, pp.  267-285. http://gdmltest.u-ga.fr/item/1256048239/