We construct a defining function for a convex domain in Cn that we use to prove that the solution-operator of Henkin-Romanov for the ∂-equation is bounded in L1 and L∞-norms with a weight that reflects not only how near the point is to the boundary of the domain but also how convex the domain is near the point. We refine and localize the weights that Polking uses in [Po] for the same type of domains because they depend only on the Euclidean distance to the boudary and don't take into account the geometry of the domain.
@article{urn:eudml:doc:41764,
title = {L1 and L$\infty$-estimates with a local weight for the $\partial$-equation on convex domains in Cn.},
journal = {Publicacions Matem\`atiques},
volume = {36},
year = {1992},
pages = {989-999},
mrnumber = {MR1210031},
zbl = {0791.35085},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41764}
}
Tugores, Francesc. L1 and L∞-estimates with a local weight for the ∂-equation on convex domains in Cn.. Publicacions Matemàtiques, Tome 36 (1992) pp. 989-999. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41764/