Variation for singular integrals on Lipschitz graphs: $L^{p}$ and endpoint estimates

@article{Mas2011VariationFS,
  title={Variation for singular integrals on Lipschitz graphs: \$L^\{p\}\$ and endpoint estimates},
  author={Albert Mas},
  journal={Transactions of the American Mathematical Society},
  year={2011},
  volume={365},
  pages={5759-5781}
}
  • A. Mas
  • Published 4 October 2011
  • Mathematics
  • Transactions of the American Mathematical Society
Let 0 2, we prove that the r-variation and oscillation for Calder\'on-Zygmund singular integrals with odd kernel are bounded operators in L^p(H) for 1<p finite, from L^1(H) to weak-L^1(H), and from the space of bounded H-measurable functions to BMO(H). Concerning the first endpoint estimate, we actually show that such operators are bounded from the space of finite complex Radon measures in R^d to weak-L^1(H). 
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