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• # Artykuł - szczegóły

## Annales Polonici Mathematici

2008 | 94 | 1 | 79-87

## Interpolating sequences, Carleson measures and Wirtinger inequality

EN

### Abstrakty

EN
Let S be a sequence of points in the unit ball 𝔹 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 $μ_{S}:= ∑_{a∈S} (1-|a|²)ⁿ δ_{a}$ is bounded, by use of the Wirtinger inequality. Conversely, if X is an analytic subset of 𝔹 such that any δ -separated sequence S has its associated measure $μ_{S}$ bounded by C/δⁿ, then X is the zero set of a function in the Nevanlinna class of 𝔹.
As an easy consequence, we prove that if S is a dual bounded sequence in $H^{p}(𝔹)$, then $μ_{S}$ is a Carleson measure, which gives a short proof in one variable of a theorem of L. Carleson and in several variables of a theorem of P. Thomas.

79-87

wydano
2008

### Twórcy

autor
• UFR Mathématique et Informatique, Université de Bordeaux I, 351, Cours de la Libération, 33405 Talence, France