Necessary condition for the L2 boundedness of the Riesz transform on Heisenberg groups
Dąbrowski, D., & Villa, M. (2023). Necessary condition for the L2 boundedness of the Riesz transform on Heisenberg groups. Mathematical Proceedings of the Cambridge Philosophical Society, 175(2), 445-458. https://doi.org/10.1017/S0305004123000245
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2023Copyright
© 2023 Cambridge University Press
Let μ be a Radon measure on the nth Heisenberg group Hn. In this note we prove that if the (2n+1) -dimensional (Heisenberg) Riesz transform on Hn is L2(μ) -bounded, and if μ(F)=0 for all Borel sets with dimH(F)≤2 , then μ must have (2n+1) -polynomial growth. This is the Heisenberg counterpart of a result of Guy David from [ Dav91 ].
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Cambridge University Press (CUP)ISSN Search the Publication Forum
0305-0041Keywords
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DAMIAN DĄBROWSKI †§ MICHELE VILLA ‡§ † Supported by Spanish Ministry of Economy and Competitiveness, through the María de Maeztu Programme for Units of Excellence in R&D (grant MDM-2014-0445). Partially supported by the Catalan Agency for Management of University and Research Grants (grant 2017-SGR-0395), and by the Spanish Ministry of Science, Innovation and Universities (grant MTM-2016-77635- ...
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