Boundedness from H^1 to L^1 of Riesz transforms on a Lie group of exponential growth

Details Boundedness from H^1 to L^1 of Riesz transforms on a Lie group of exponential growth Boundedness from H^1 to L^1 of Riesz transforms on a Lie group of exponential growth

2007-09-27

arxiv.org/abs/0709.4347v1

Mathematics

Classical Analysis and ODEs

This paper will be published in the "Annales de l'Institut Fourier"

Scientific paper

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 $\Delta=-(X_0^2+X_1^2+X_2^2)$. In this paper we consider the first order Riesz transforms $R_i=X_i\Delta^{-1/2}$ and $S_i=\Delta^{-1/2}X_i$, 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 $T_{ij}=X_i\Delta^{-1}X_j$ are bounded from $H^1$ to $L^1$, while the Riesz transforms $S_{ij}=\Delta^{-1}X_iX_j$ and $R_{ij}=X_iX_j\Delta^{-1}$ are not.

Affiliated with

Also associated with

No associations

Rating

Boundedness from H^1 to L^1 of Riesz transforms on a Lie group of exponential growth does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Boundedness from H^1 to L^1 of Riesz transforms on a Lie group of exponential growth, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Boundedness from H^1 to L^1 of Riesz transforms on a Lie group of exponential growth will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-481493