Interpolating sequences, Carleson measures and Wirtinger inequality

• Autorzy: Eric Amar
• Języki publikacji: 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.

Kategorie tematyczne

• 32A35: H p -spaces, Nevanlinna spaces
• 42B30: H p -spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2008
• Tom: 94
• Numer: 1
• Strony: 79-87

Daty

wydano

2008

Twórcy

autor

Eric Amar

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

Identyfikatory

DOI

10.4064/ap94-1-6