Weighted endpoint estimates for commutators of multilinear fractional integral operators

Xuefang Yan; Limei Xue; Wenming Li

Czechoslovak Mathematical Journal (2012)

  • Volume: 62, Issue: 2, page 347-359
  • ISSN: 0011-4642

Abstract

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Let m be a positive integer, 0 < α < m n , b → = ( b 1 , ⋯ , b m ) ∈ BMO m . We give sufficient conditions on weights for the commutators of multilinear fractional integral operators ℐ α b → to satisfy a weighted endpoint inequality which extends the result in D. Cruz-Uribe, A. Fiorenza: Weighted endpoint estimates for commutators of fractional integrals, Czech. Math. J. 57 (2007), 153–160. We also give a weighted strong type inequality which improves the result in X. Chen, Q. Xue: Weighted estimates for a class of multilinear fractional type operators, J. Math. Anal. Appl., 362, (2010), 355–373.

How to cite

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Yan, Xuefang, Xue, Limei, and Li, Wenming. "Weighted endpoint estimates for commutators of multilinear fractional integral operators." Czechoslovak Mathematical Journal 62.2 (2012): 347-359. <http://eudml.org/doc/246320>.

@article{Yan2012,
abstract = {Let $m$ be a positive integer, $0<\alpha <mn$, $\vec\{b\}=(b_\{1\},\cdots ,b_\{m\})\in \{\rm BMO\}^m$. We give sufficient conditions on weights for the commutators of multilinear fractional integral operators $\mathcal \{I\}^\{\vec\{b\}\}_\{\alpha \}$ to satisfy a weighted endpoint inequality which extends the result in D. Cruz-Uribe, A. Fiorenza: Weighted endpoint estimates for commutators of fractional integrals, Czech. Math. J. 57 (2007), 153–160. We also give a weighted strong type inequality which improves the result in X. Chen, Q. Xue: Weighted estimates for a class of multilinear fractional type operators, J. Math. Anal. Appl., 362, (2010), 355–373.},
author = {Yan, Xuefang, Xue, Limei, Li, Wenming},
journal = {Czechoslovak Mathematical Journal},
keywords = {multilinear fractional integral operators; commutator; BMO; weight; maximal operators; multilinear fractional integral operator; commutator; BMO; maximal operator},
language = {eng},
number = {2},
pages = {347-359},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Weighted endpoint estimates for commutators of multilinear fractional integral operators},
url = {http://eudml.org/doc/246320},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Yan, Xuefang
AU - Xue, Limei
AU - Li, Wenming
TI - Weighted endpoint estimates for commutators of multilinear fractional integral operators
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 2
SP - 347
EP - 359
AB - Let $m$ be a positive integer, $0<\alpha <mn$, $\vec{b}=(b_{1},\cdots ,b_{m})\in {\rm BMO}^m$. We give sufficient conditions on weights for the commutators of multilinear fractional integral operators $\mathcal {I}^{\vec{b}}_{\alpha }$ to satisfy a weighted endpoint inequality which extends the result in D. Cruz-Uribe, A. Fiorenza: Weighted endpoint estimates for commutators of fractional integrals, Czech. Math. J. 57 (2007), 153–160. We also give a weighted strong type inequality which improves the result in X. Chen, Q. Xue: Weighted estimates for a class of multilinear fractional type operators, J. Math. Anal. Appl., 362, (2010), 355–373.
LA - eng
KW - multilinear fractional integral operators; commutator; BMO; weight; maximal operators; multilinear fractional integral operator; commutator; BMO; maximal operator
UR - http://eudml.org/doc/246320
ER -

References

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