## Tohoku Mathematical Journal

### Hardy spaces and maximal operators on real rank one semisimple Lie groups, I

Takeshi Kawazoe

#### Abstract

Let $G$ be a real rank one connected semisimple Lie group with finite center. As well-known the radial, heat, and Poisson maximal operators satisfy the $L^p$-norm inequalities for any $p>1$ and a weak type $L^1$ estimate. The aim of this paper is to find a subspace of $L^1(G)$ from which they are bounded into $L^1(G)$. As an analogue of the atomic Hardy space on the real line, we introduce an atomic Hardy space on $G$ and prove that these maximal operators with suitable modifications are bounded from the atomic Hardy space on $G$ to $L^1(G)$.

#### Article information

Source
Tohoku Math. J. (2), Volume 52, Number 1 (2000), 1-18.

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178224654

Digital Object Identifier
doi:10.2748/tmj/1178224654

Mathematical Reviews number (MathSciNet)
MR1740539

Zentralblatt MATH identifier
0952.22004

#### Citation

Kawazoe, Takeshi. Hardy spaces and maximal operators on real rank one semisimple Lie groups, I. Tohoku Math. J. (2) 52 (2000), no. 1, 1--18. doi:10.2748/tmj/1178224654. https://projecteuclid.org/euclid.tmj/1178224654

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