Partial retractions for weighted Hardy spaces

Sergei Kisliakov; Quanhua Xu

Partial retractions for weighted Hardy spaces

Sergei Kisliakov^*
, Quanhua Xu

^*Corresponding author for this work

St. Petersburg Branch
UMR de Mathématiques

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

Let 1 ≤ p ≤ ∞ and let w₀, w₁ be two weights on the unit circle such that log(w₀w^-1₁) ∈ BMO. We prove that the couple (H_p(w₀), H_p(w₁)) of weighted Hardy spaces is a partial retract of (L_p(w₀), L_p(w₁)). This completes previous work of the authors. More generally, we have a similar result for finite families of weighted Hardy spaces. We include some applications to interpolation.

Original language	English
Pages (from-to)	251-264
Number of pages	14
Journal	Studia Mathematica
Volume	138
Issue number	3
State	Published - 2000
Externally published	Yes

Keywords

BMO
Interpolation
Partial retraction
Weighted Hardy space

Cite this

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title = "Partial retractions for weighted Hardy spaces",

abstract = "Let 1 ≤ p ≤ ∞ and let w0, w1 be two weights on the unit circle such that log(w0w-11) ∈ BMO. We prove that the couple (Hp(w0), Hp(w1)) of weighted Hardy spaces is a partial retract of (Lp(w0), Lp(w1)). This completes previous work of the authors. More generally, we have a similar result for finite families of weighted Hardy spaces. We include some applications to interpolation.",

keywords = "BMO, Interpolation, Partial retraction, Weighted Hardy space",

author = "Sergei Kisliakov and Quanhua Xu",

year = "2000",

language = "英语",

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journal = "Studia Mathematica",

issn = "0039-3223",

publisher = "Institute of Mathematics. Polish Academy of Sciences",

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T1 - Partial retractions for weighted Hardy spaces

AU - Kisliakov, Sergei

AU - Xu, Quanhua

PY - 2000

Y1 - 2000

N2 - Let 1 ≤ p ≤ ∞ and let w0, w1 be two weights on the unit circle such that log(w0w-11) ∈ BMO. We prove that the couple (Hp(w0), Hp(w1)) of weighted Hardy spaces is a partial retract of (Lp(w0), Lp(w1)). This completes previous work of the authors. More generally, we have a similar result for finite families of weighted Hardy spaces. We include some applications to interpolation.

AB - Let 1 ≤ p ≤ ∞ and let w0, w1 be two weights on the unit circle such that log(w0w-11) ∈ BMO. We prove that the couple (Hp(w0), Hp(w1)) of weighted Hardy spaces is a partial retract of (Lp(w0), Lp(w1)). This completes previous work of the authors. More generally, we have a similar result for finite families of weighted Hardy spaces. We include some applications to interpolation.

KW - BMO

KW - Interpolation

KW - Partial retraction

KW - Weighted Hardy space

UR - https://www.scopus.com/pages/publications/0040809154

M3 - 文章

AN - SCOPUS:0040809154

SN - 0039-3223

VL - 138

SP - 251

EP - 264

JO - Studia Mathematica

JF - Studia Mathematica

IS - 3

ER -

Partial retractions for weighted Hardy spaces

Abstract

Keywords

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