Report
Necessary condition for the $L^2$ boundedness of the Riesz transform on Heisenberg groups
| العنوان: | Necessary condition for the $L^2$ boundedness of the Riesz transform on Heisenberg groups |
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| المؤلفون: | Dąbrowski, Damian, Villa, Michele |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Classical Analysis and ODEs, Mathematics - Metric Geometry, 42B20 (Primary) 43A80, 28A75, 35R03 (Secondary) |
| الوصف: | Let $\mu$ be a Radon measure on the $n$-th Heisenberg group $\mathbb{H}^n$. In this note we prove that if the $(2n+1)$-dimensional (Heisenberg) Riesz transform on $\mathbb{H}^n$ is $L^2(\mu)$-bounded, and if $\mu(F)=0$ for all Borel sets with $\dim_H(F)\leq 2$, then $\mu$ must have $(2n+1)$-polynomial growth. This is the Heisenberg counterpart of a result of Guy David from 1991. Comment: 14 pages |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1017/S0305004123000245 |
| URL الوصول: | http://arxiv.org/abs/2004.01117 |
| رقم الانضمام: | edsarx.2004.01117 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1017/S0305004123000245 |
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