Interpolation between H^p spaces and non-commutative generalizations (II).

Título inglés	Interpolation between Hp spaces and non-commutative generalizations (II).
Título español	Interpolación entre espacios Hp y generalizaciones no conmutativas (II).
Autor/es	Pisier, Gilles
Organización	Dep. Math. Texas A&M Univ., College Station (Texas), Estados Unidos;Univ. Paris VI Pierre et Marie Curie, París, Francia
Revista	0213-2230
Publicación	1993, 9 (2): 281-291, 10 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	We continue an investigation started in a preceding paper. We discuss tha classical result of Carleson connecting Carleson measures with the ∂-equation in a slightly more abstract framework than usual. We also consider a more recent result of Peter Jones which shows the existence of a solution for the ∂-equation, which satisfies simultaneously a good L∞ estimate and a good L1 estimate. This appears as a special case of our main result which can be stated as follows: Let (Ω, A, μ) be any measure space. Consider a bounded operator u: H1 → L1(μ). Assume that on one hand u admits an extension u1: L1 → L1(μ) bounded with norm C1, and on the other hand that u admits an extension u∞: L∞ → L∞(μ) bounded with norm C∞. Then u admits an extension u' which is bounded simultaneously from L1 into L1(μ) and from L∞ into L∞(μ) and satisfies ||u': L∞ → L∞(μ)|| ≤ C C∞ ||u': L1 → L1(μ)|| ≤ C C1 where C is a numerical constant.
Clasificación UNESCO	120201
Palabras clave español	Espacios de Hardy ; Espacios LP ; Desigualdades ; Interpolación ; Funciones analíticas
Código MathReviews	MR1232844
Código Z-Math	Zbl 0788.46071
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