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𝒞 k -regularity for the ¯ -equation with a support condition

Shaban Khidr, Osama Abdelkader (2017)

Czechoslovak Mathematical Journal

Let D be a 𝒞 d q -convex intersection, d 2 , 0 q n - 1 , in a complex manifold X of complex dimension n , n 2 , and let E be a holomorphic vector bundle of rank N over X . In this paper, 𝒞 k -estimates, k = 2 , 3 , , , for solutions to the ¯ -equation with small loss of smoothness are obtained for E -valued ( 0 , s ) -forms on D when n - q s n . In addition, we solve the ¯ -equation with a support condition in 𝒞 k -spaces. More...

Approximation de fonctions holomorphes d'un nombre infini de variables

László Lempert (1999)

Annales de l'institut Fourier

Soit X un espace de Banach complexe, et notons B ( R ) X la boule de rayon R centrée en 0 . On considère le problème d’approximation suivant: étant donnés 0 < r < R , ϵ > 0 et une fonction f holomorphe dans B ( R ) , existe-t-il toujours une fonction g , holomorphe dans X , telle que | f - g | < ϵ sur B ( r ) ? On démontre que c’est bien le cas si X est l’espace l 1 des suites sommables.

Banach space properties of strongly tight uniform algebras

Scott Saccone (1995)

Studia Mathematica

We use the work of J. Bourgain to show that some uniform algebras of analytic functions have certain Banach space properties. If X is a Banach space, we say X is strongif X and X* have the Dunford-Pettis property, X has the Pełczyński property, and X* is weakly sequentially complete. Bourgain has shown that the ball-algebras and the polydisk-algebras are strong Banach spaces. Using Bourgain’s methods, Cima and Timoney have shown that if K is a compact planar set and A is R(K) or A(K), then A and...

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