RESEARCH ARTICLE

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

  • Jing ZHANG 1,2 ,
  • Huoxiong WU , 1
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  • 1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • 2. School of Mathematics and Statistics, Yili Normal College, Yining 835000, China

Received date: 21 Nov 2014

Accepted date: 02 Mar 2015

Published date: 18 Apr 2016

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

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.

Cite this article

Jing ZHANG , Huoxiong WU . Oscillation and variation inequalities for singular integrals and commutators on weighted Morrey spaces[J]. Frontiers of Mathematics in China, 2016 , 11(2) : 423 -447 . DOI: 10.1007/s11464-015-0462-2

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