# Interpolation between Hp spaces and non-commutative generalizations (II).

Revista Matemática Iberoamericana (1993)

- Volume: 9, Issue: 2, page 281-291
- ISSN: 0213-2230

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topPisier, Gilles. "Interpolation between Hp spaces and non-commutative generalizations (II).." Revista Matemática Iberoamericana 9.2 (1993): 281-291. <http://eudml.org/doc/39438>.

@article{Pisier1993,

abstract = {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 C1where C is a numerical constant.},

author = {Pisier, Gilles},

journal = {Revista Matemática Iberoamericana},

keywords = {Espacios de Hardy; Espacios LP; Desigualdades; Interpolación; Funciones analíticas; Carleson measures; -equation},

language = {eng},

number = {2},

pages = {281-291},

title = {Interpolation between Hp spaces and non-commutative generalizations (II).},

url = {http://eudml.org/doc/39438},

volume = {9},

year = {1993},

}

TY - JOUR

AU - Pisier, Gilles

TI - Interpolation between Hp spaces and non-commutative generalizations (II).

JO - Revista Matemática Iberoamericana

PY - 1993

VL - 9

IS - 2

SP - 281

EP - 291

AB - 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 C1where C is a numerical constant.

LA - eng

KW - Espacios de Hardy; Espacios LP; Desigualdades; Interpolación; Funciones analíticas; Carleson measures; -equation

UR - http://eudml.org/doc/39438

ER -

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