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

Título inglés Semi-global solutions of ∂b with Lp (1 ≤ p ≤ ∞) bounds on strongly pseudoconvex real hypersurfaces in Cn (n ≥ 3).
Título español Soluciones semiglobales de ∂b con acotaciones Lp (1 ≤ p ≤ ∞) sobre hipersuperficies reales fuertemente pseudoconvexas en Cn (n ≥ 3).
Autor/es Chang, C. H. ; Lee, H. P.
Organización Inst. Math. Acad. Sinica, Taipei, Taiwan
Revista 0214-1493
Publicación 1999, 43 (2): 535-570, 25 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés 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} Ì 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.
Código MathReviews MR1744621
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