Let M be an open subset of a compact strongly pseudoconvex hypersurface {ρ = 0} defined by M = D × Cn-m ∩ {ρ = 0}, where 1 ≤ m ≤ n-2, D = {σ(z1, ..., zm) < 0} ⊂ Cm is strongly pseudoconvex in Cm. For ∂b closed (0, q) forms f on M, we prove the semi-global existence theorem for ∂b if 1 ≤ q ≤ n-m-2, or if q = n - m - 1 and f satisfies an additional “moment condition”. Most importantly, the solution operator satisfies Lp estimates for 1 ≤ p ≤ ∞ with p = 1 and ∞ included.
@article{urn:eudml:doc:41602,
title = {Semi-global solutions of $\partial$b with Lp (1 $\leq$ p $\leq$ $\infty$) bounds on strongly pseudoconvex real hypersurfaces in Cn (n $\geq$ 3).},
journal = {Publicacions Matem\`atiques},
volume = {43},
year = {1999},
pages = {535-570},
mrnumber = {MR1744621},
zbl = {0954.32027},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41602}
}
Chang, C. H.; Lee, H. P. Semi-global solutions of ∂b with Lp (1 ≤ p ≤ ∞) bounds on strongly pseudoconvex real hypersurfaces in Cn (n ≥ 3).. Publicacions Matemàtiques, Tome 43 (1999) pp. 535-570. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41602/