Représentation des fonctions de BMO et solutions dé l'équation ...b.
Non division dans A ... (...).
Sur un problème de W. Rudin concernant les fonctions holomorphes et borneés
On linear extension for interpolating sequences
Let A be a uniform algebra on X and σ a probability measure on X. We define the Hardy spaces and the interpolating sequences S in the p-spectrum of σ. We prove, under some structural hypotheses on A and σ, that if S is a “dual bounded” Carleson sequence, then S is -interpolating with a linear extension operator for s < p, provided that either p = ∞ or p ≤ 2. In the case of the unit ball of ℂⁿ we find, for instance, that if S is dual bounded in then S is -interpolating with a linear...
Outer ideals and division in
Extension de formes fermées et solutions de l’équation
Estimées Lipschitz dans les domaines convexes de type fini de C.
Using explicit integral formulas introduced by Skoda, we obtain Hölder estimates for the δ-equation in convex domains of finite type in C.
On the Toëplitz corona problem.
The aim of this note is to characterize the vectors g = (g, . . . ,g) of bounded holomorphic functions in the unit ball or in the unit polydisk of C such that the Corona is true for them in terms of the H Corona for measures on the boundary.
Interpolating sequences, Carleson measures and Wirtinger inequality
Let S be a sequence of points in the unit ball of ℂⁿ which is separated for the hyperbolic distance and contained in the zero set of a Nevanlinna function. We prove that the associated measure is bounded, by use of the Wirtinger inequality. Conversely, if X is an analytic subset of such that any δ -separated sequence S has its associated measure bounded by C/δⁿ, then X is the zero set of a function in the Nevanlinna class of . As an easy consequence, we prove that if S is a dual bounded sequence...
Mesures de Carleson d’ordre et solutions au bord de l’équation
Uniform minimality, unconditionality and interpolation in backward shift invariant subspaces
We discuss relations between uniform minimality, unconditionality and interpolation for families of reproducing kernels in backward shift invariant subspaces. This class of spaces contains as prominent examples the Paley-Wiener spaces for which it is known that uniform minimality does in general neither imply interpolation nor unconditionality. Hence, contrarily to the situation of standard Hardy spaces (and of other scales of spaces), changing the size of the space seems necessary to deduce unconditionality...
A notion of extremal analytic discs related to interpolation in the ball.
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