Spaces H^1 and BMO on ax+b-groups
Classical Analysis and ODEs
2008-04-30 v1
Abstract
Let S be the semidirect product of R^d and R^+ endowed with the Riemannian symmetric space metric and the right Haar measure: this is a Lie group of exponential growth. In this paper we define an Hardy space H^1 and a BMO space in this context. We prove that the functions in BMO satisfy the John-Nirenberg inequality and that BMO may be identified with the dual space of H^1. We then prove that singular integral operators which satisfy a suitable integral Hormander condition are bounded from H^1 to L^1 and from L^{\infty} to BMO. We also study the real interpolation between H^1, BMO and the L^p spaces.
Cite
@article{arxiv.0804.4615,
title = {Spaces H^1 and BMO on ax+b-groups},
author = {Maria Vallarino},
journal= {arXiv preprint arXiv:0804.4615},
year = {2008}
}