# Semi-global solutions of ∂b with Lp (1 ≤ p ≤ ∞) bounds on strongly pseudoconvex real hypersurfaces in Cn (n ≥ 3).

• Volume: 43, Issue: 2, page 535-570
• ISSN: 0214-1493

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## Abstract

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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) &lt; 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.

## How to cite

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Chang, C. H., and Lee, H. P.. "Semi-global solutions of ∂b with Lp (1 ≤ p ≤ ∞) bounds on strongly pseudoconvex real hypersurfaces in Cn (n ≥ 3).." Publicacions Matemàtiques 43.2 (1999): 535-570. <http://eudml.org/doc/41602>.

@article{Chang1999,
abstract = {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) &lt; 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.},
author = {Chang, C. H., Lee, H. P.},
journal = {Publicacions Matemàtiques},
keywords = {tangential Cauchy-Riemann equation; semi-global solvability with estimate; CR manifold solution operator; closed forms; Henkin kernel; Leray section},
language = {eng},
number = {2},
pages = {535-570},
title = {Semi-global solutions of ∂b with Lp (1 ≤ p ≤ ∞) bounds on strongly pseudoconvex real hypersurfaces in Cn (n ≥ 3).},
url = {http://eudml.org/doc/41602},
volume = {43},
year = {1999},
}

TY - JOUR
AU - Chang, C. H.
AU - Lee, H. P.
TI - Semi-global solutions of ∂b with Lp (1 ≤ p ≤ ∞) bounds on strongly pseudoconvex real hypersurfaces in Cn (n ≥ 3).
JO - Publicacions Matemàtiques
PY - 1999
VL - 43
IS - 2
SP - 535
EP - 570
AB - 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) &lt; 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.
LA - eng
KW - tangential Cauchy-Riemann equation; semi-global solvability with estimate; CR manifold solution operator; closed forms; Henkin kernel; Leray section
UR - http://eudml.org/doc/41602
ER -

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