Science China Mathematics

, Volume 61, Issue 3, pp 517–534 | Cite as

Weighted weak type (1, 1) estimate for the Christ-Journé type commutator

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Abstract

Let K be the Calderón-Zygmund convolution kernel on Rd (d ≥ 2). Christ and Journé de0ned the commutator associated with K and a ∈ L1(ℝd) by
$${T_a}f(x) = p.v.{\smallint _{{ℝ^d}}}K(x - y){m_{x,y}}af(y)dy$$
(1)
, which is an extension of the classical Calderón commutator. In this paper, we show that Ta is weighted weak type (1, 1) bounded with A1 weight for d ≥ 2.

Keywords

Christ-Journé type commutator weighted weak type (1, 1) A1 weight 

MSC(2010)

42B20 

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Notes

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11371057, 11471033 and 11571160), Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20130003110003), and the Fundamental Research Funds for the Central Universities (Grant No. 2014KJJCA10). The authors express their gratitude to the referees for their very careful reading and valuable suggestions.

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesBeijing Normal UniversityBeijingChina
  2. 2.Institute for Advanced Study in MathematicsHarbin Institute of TechnologyHarbinChina

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