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      Singular integrals on regular curves in the Heisenberg group

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          Abstract

          We show that smooth \(-1\)-homogeneous horizontally odd kernels in the Heisenberg group induce Calder\'on-Zygmund operators on regular curves. This extends a theorem of G. David from 1984 to the Heisenberg group.

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          Most cited references21

          • Record: found
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          Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains

          Gregory Verchota (1984)
          Article 0 comments Cited 97 times – based on 0 reviews     Review now
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            L'integrale de Cauchy Definit un Operateur Borne sur L 2 Pour Les Courbes Lipschitziennes

            R R Coifman, Y. Meyer, A. McIntosh (1982)
            Article 0 comments Cited 62 times – based on 0 reviews     Review now
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              Rectifiable sets and the Traveling Salesman Problem

              Peter Jones (1990)
              Article 0 comments Cited 58 times – based on 0 reviews     Review now
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                Author and article information

                Journal
                Publication date Created: 08 November 2019
                Article
                ArXiV ID: 1911.03223
                SO-VID: c671134a-64c5-416d-9486-56f214256976
                License:

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                ACM classes 42B20 (primary), 43A80, 28A75, 35R03 (secondary)
                Report No BCSim-2019-s12
                Comments 60 pages
                Categories math.CA math.FA math.MG

                ScienceOpen disciplines: Functional analysis,Geometry & Topology,Mathematics
                Data availability:
                ScienceOpen disciplines: Functional analysis, Geometry & Topology, Mathematics

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