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Oscillation and variation inequalities for singular integrals and commutators on weighted Morrey spaces

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Abstract

This paper is devoted to investigating the bounded behaviors of the oscillation and variation operators for Calderón-Zygmund singular integrals and the corresponding commutators on the weighted Morrey spaces. We establish several criterions of boundedness, which are applied to obtain the corresponding bounds for the oscillation and variation operators of Hilbert transform, Hermitian Riesz transform and their commutators with BMO functions, or Lipschitz functions on weighted Morrey spaces.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    Jing Zhang & Huoxiong Wu

  2. School of Mathematics and Statistics, Yili Normal College, Yining, 835000, China

    Jing Zhang

Authors
  1. Jing Zhang
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  2. Huoxiong Wu
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Correspondence to Huoxiong Wu.

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Zhang, J., Wu, H. Oscillation and variation inequalities for singular integrals and commutators on weighted Morrey spaces. Front. Math. China 11, 423–447 (2016). https://doi.org/10.1007/s11464-015-0462-2

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  • DOI: https://doi.org/10.1007/s11464-015-0462-2

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