A Weak-Type Estimate for Commutators

@article{Grafakos2012AWE,
  title={A Weak-Type Estimate for Commutators},
  author={Loukas Grafakos and Petr Honz{\'i}k},
  journal={International Mathematics Research Notices},
  year={2012},
  volume={2012},
  pages={4785-4796}
}
Let K be a smooth Calderón-Zygmund convolution kernel on R and suppose we are given a function a ∈ L∞. The two-dimensional commutator Tf(x) = ∫ K(x− y)f(y) ∫ [x,y] a(z) dz dy was shown to be bounded on L(R), p > 1 by Christ and Journé [1]. In this article, we show that this operator is also of weak type (1, 1). 
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University of Missouri, Columbia MO 65211, USA E-mail address: grafakosl@missouri
  • University of Missouri, Columbia MO 65211, USA E-mail address: grafakosl@missouri
CZ -115 67 Praha 1, Czech Republic E-mail address: honzik@gmail
  • CZ -115 67 Praha 1, Czech Republic E-mail address: honzik@gmail