Singular integrals associated to the Laplacian on the affine group$ax+b$

G. I. Gaudry School of Information Science and Technology, The Flinders University of South Austrlia T. Qian Department of Mathematics, University of New England P. Sjögren Department of Mathematics, Chalmers University of Technology

TBD mathscidoc:1701.332773

Arkiv for Matematik, 30, (1), 259-281, 1991.7
We consider singular integral operators of the form (a)$Z$_{1}L^{−1}Z_{2}, (b)$Z$_{1}Z_{2}L^{−1}, and (c)$L$^{−1}Z_{1}Z_{2}, where$Z$_{1}and$Z$_{2}are nonzero right-invariant vector fields, and$L$is the$L$^{2}-closure of a canonical Laplacian. The operators (a) are shown to be bounded on$L$^{p}for all$p$∈(1, ∞) and of weak type (1, 1), whereas all of the operators in (b) and (c) are not of weak type ($p, p$) for any$p$∈[1, ∞).
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@inproceedings{g.1991singular,
  title={Singular integrals associated to the Laplacian on the affine group$ax+b$},
  author={G. I. Gaudry, T. Qian, and P. Sjögren},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203538168366582},
  booktitle={Arkiv for Matematik},
  volume={30},
  number={1},
  pages={259-281},
  year={1991},
}
G. I. Gaudry, T. Qian, and P. Sjögren. Singular integrals associated to the Laplacian on the affine group$ax+b$. 1991. Vol. 30. In Arkiv for Matematik. pp.259-281. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203538168366582.
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