Boundedness from H^1 to L^1 of Riesz transforms on a Lie group of exponential growth
| dc.creator | Sjögren, Peter | |
| dc.creator | Vallarino, Maria | |
| dc.date | 2007-09-27 | |
| dc.date.accessioned | 2026-07-07T08:32:34Z | |
| dc.date.available | 2026-07-07T08:32:34Z | |
| dc.description | Let $G$ be the Lie group given by the semidirect product of $R^2$ and $R^+$ endowed with the Riemannian symmetric space structure. Let $X_0, X_1, X_2$ be a distinguished basis of left-invariant vector fields of the Lie algebra of $G$ and define the Laplacian $Δ=-(X_0^2+X_1^2+X_2^2)$. In this paper we consider the first order Riesz transforms $R_i=X_iΔ^{-1/2}$ and $S_i=Δ^{-1/2}X_i$, for $i=0,1,2$. We prove that the operators $R_i$, but not the $S_i$, are bounded from the Hardy space $H^1$ to $L^1$. We also show that the second order Riesz transforms $T_{ij}=X_iΔ^{-1}X_j$ are bounded from $H^1$ to $L^1$, while the Riesz transforms $S_{ij}=Δ^{-1}X_iX_j$ and $R_{ij}=X_iX_jΔ^{-1}$ are not. | |
| dc.description | This paper will be published in the "Annales de l'Institut Fourier" | |
| dc.identifier | https://arxiv.org/abs/0709.4347 | |
| dc.identifier | http://arxiv.org/abs/0709.4347 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138834 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 43A80, 42B20, 42B30, 22E30 | |
| dc.title | Boundedness from H^1 to L^1 of Riesz transforms on a Lie group of exponential growth | |
| dc.type | text |