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Uniform estimates for the Cauchy-Riemann equation on q -convex wedges

Christine Laurent-ThiébautJurgen Leiterer — 1993

Annales de l'institut Fourier

We study the -equation with Hölder estimates in q -convex wedges of n by means of integral formulas. If D n is defined by some inequalities { ρ i 0 } , where the real hypersurfaces { ρ i = 0 } are transversal and any nonzero linear combination with nonnegative coefficients of the Levi form of the ρ i ’s have at least ( q + 1 ) positive eigenvalues, we solve the equation f = g for each continuous ( n , r ) -closed form g in D , n - q r n , with the following estimates: if d denotes the distance to the boundary of D and if d β g is bounded, then for all ϵ > 0 ,...

Analytic extension from non-pseudoconvex boundaries and A ( D ) -convexity

Christine Laurent-ThiébautEgmon Porten — 2003

Annales de l’institut Fourier

Let D n , n 2 , be a domain with C 2 -boundary and K D be a compact set such that D K is connected. We study univalent analytic extension of CR-functions from D K to parts of D . Call K CR-convex if its A ( D ) -convex hull, A ( D ) - hull ( K ) , satisfies K = D A ( D ) - hull ( K ) ( A ( D ) denoting the space of functions, which are holomorphic on D and continuous up to D ). The main theorem of the paper gives analytic extension to D A ( D ) - hull ( K ) , if K is CR- convex.

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