Necessary condition for the L2 boundedness of the Riesz transform on Heisenberg groups
Abstract
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 ].
Main Authors
Format
Articles
Research article
Published
2023
Series
Subjects
Publication in research information system
Publisher
Cambridge University Press (CUP)
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202402232102Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
0305-0041
DOI
https://doi.org/10.1017/S0305004123000245
Language
English
Published in
Mathematical Proceedings of the Cambridge Philosophical Society
Citation
- 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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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-P).
‡ Supported by The Maxwell Institute Graduate School in Analysis and its Applications, a Centre for Doctoral Training funded by the UK Engineering and Physical Sciences Research Council (grant EP/L016508/01), the Scottish Funding Council, Heriot-Watt University and the University of Edinburgh.
§ Partially supported by the grant 346300 for IMPAN from the Simons Foundation and the matching 2015-2019 Polish MNiSW fund.
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