Partial retractions for weighted Hardy spaces

Sergei Kisliakov; Quanhua Xu

Studia Mathematica (2000)

  • Volume: 138, Issue: 3, page 251-264
  • ISSN: 0039-3223

Abstract

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Let 1 ≤ p ≤ ∞ and let w 0 , w 1 be two weights on the unit circle such that l o g ( w 0 w 1 - 1 ) ∈ B M O . We prove that the couple ( H p ( w 0 ) , H p ( w 1 ) ) of weighted Hardy spaces is a partial retract of ( L p ( w 0 ) , L p ( w 1 ) ) . 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.

How to cite

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Kisliakov, Sergei, and Xu, Quanhua. "Partial retractions for weighted Hardy spaces." Studia Mathematica 138.3 (2000): 251-264. <http://eudml.org/doc/216703>.

@article{Kisliakov2000,
abstract = {Let 1 ≤ p ≤ ∞ and let $w_0, w_1$ be two weights on the unit circle such that $log(w_0w_1^\{-1\})∈ BMO$. We prove that the couple $(H_p(w_0), H_p(w_1))$ of weighted Hardy spaces is a partial retract of $(L_p(w_0), L_p(w_1))$. 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.},
author = {Kisliakov, Sergei, Xu, Quanhua},
journal = {Studia Mathematica},
keywords = {partial retraction; interpolation; weighted Hardy space; BMO; Hardy space; weight},
language = {eng},
number = {3},
pages = {251-264},
title = {Partial retractions for weighted Hardy spaces},
url = {http://eudml.org/doc/216703},
volume = {138},
year = {2000},
}

TY - JOUR
AU - Kisliakov, Sergei
AU - Xu, Quanhua
TI - Partial retractions for weighted Hardy spaces
JO - Studia Mathematica
PY - 2000
VL - 138
IS - 3
SP - 251
EP - 264
AB - Let 1 ≤ p ≤ ∞ and let $w_0, w_1$ be two weights on the unit circle such that $log(w_0w_1^{-1})∈ BMO$. We prove that the couple $(H_p(w_0), H_p(w_1))$ of weighted Hardy spaces is a partial retract of $(L_p(w_0), L_p(w_1))$. 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.
LA - eng
KW - partial retraction; interpolation; weighted Hardy space; BMO; Hardy space; weight
UR - http://eudml.org/doc/216703
ER -

References

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