Interpolation between Hp 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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