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Displaying similar documents to “Regularity of the tangential Cauchy-Riemann complex and applications”

Some applications of a new integral formula for ∂ ̅ b

Moulay-Youssef Barkatou (1998)

Annales Polonici Mathematici

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Let M be a smooth q-concave CR submanifold of codimension k in ℂ n . We solve locally the ∂ ̅ b -equation on M for (0,r)-forms, 0 ≤ r ≤ q-1 or n-k-q+1 ≤ r ≤ n-k, with sharp interior estimates in Hölder spaces. We prove the optimal regularity of the ∂ ̅ b -operator on (0,q)-forms in the same spaces. We also obtain L p estimates at top degree. We get a jump theorem for (0,r)-forms (r ≤ q-2 or r ≥ n-k-q+1) which are CR on a smooth hypersurface of M. We prove some generalizations of the Hartogs-Bochner-Henkin...

Hölder and L estimates for the solutions of the ∂-equation in non-smooth strictly pseudoconvex domains.

Josep M. Burgués Badía (1990)

Publicacions Matemàtiques

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Let D be a bounded strict pseudoconvex non-smooth domain in C. In this paper we prove that the estimates in L and Lipschitz classes for the solutions of the ∂-equation with L-data in regular strictly pseudoconvex domains (see [2]) are also valid for D. We also give estimates of the same type for the ∂ in the regular part of the boundary of these domains.

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

C. H. Chang, H. P. Lee (1999)

Publicacions Matemàtiques

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Let M be an open subset of a compact strongly pseudoconvex hypersurface {ρ = 0} defined by M = D × C ∩ {ρ = 0}, where 1 ≤ m ≤ n-2, D = {σ(z, ..., z) < 0} ⊂ C is strongly pseudoconvex in C. For ∂ closed (0, q) forms f on M, we prove the semi-global existence theorem for ∂ 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 L estimates for 1 ≤ p ≤ ∞ with p = 1 and ∞ included.

Trivial generators for nontrivial fibres

Linus Carlsson (2008)

Mathematica Bohemica

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Pseudoconvex domains are exhausted in such a way that we keep a part of the boundary fixed in all the domains of the exhaustion. This is used to solve a problem concerning whether the generators for the ideal of either the holomorphic functions continuous up to the boundary or the bounded holomorphic functions, vanishing at a point in ℂ n where the fibre is nontrivial, has to exceed n . This is shown not to be the case.

Hartogs theorem for forms : solvability of Cauchy-Riemann operator at critical degree

Chin-Huei Chang, Hsuan-Pei Lee (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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The Hartogs Theorem for holomorphic functions is generalized in two settings: a CR version (Theorem 1.2) and a corresponding theorem based on it for C k ∂ ¯ -closed forms at the critical degree, 0 ≤ k ≤ ∞ (Theorem 1.1). Part of Frenkel’s lemma in C k category is also proved.

The Cauchy-Riemann equations in infinite dimensions

László Lempert (1998)

Journées équations aux dérivées partielles

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I will explain basic concepts/problems of complex analysis in infinite dimensions, and survey the few approaches that are available to solve those problems.