Warianty tytułu
Języki publikacji
Abstrakty
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.
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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
79-87
Opis fizyczny
Daty
wydano
2008
Twórcy
autor
- UFR Mathématique et Informatique, Université de Bordeaux I, 351, Cours de la Libération, 33405 Talence, France
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
DOI
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-1-6