Translator Disclaimer
2000 Hardy spaces and maximal operators on real rank one semisimple Lie groups, I
Takeshi Kawazoe
Tohoku Math. J. (2) 52(1): 1-18 (2000). DOI: 10.2748/tmj/1178224654

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 $L^1(G)$.

Citation

Download Citation

Takeshi Kawazoe. "Hardy spaces and maximal operators on real rank one semisimple Lie groups, I." Tohoku Math. J. (2) 52 (1) 1 - 18, 2000. https://doi.org/10.2748/tmj/1178224654

Information

Published: 2000
First available in Project Euclid: 3 May 2007

zbMATH: 0952.22004
MathSciNet: MR1740539
Digital Object Identifier: 10.2748/tmj/1178224654

Subjects:
Primary: 22E30
Secondary: 42B25, 42B30, 46E30

Rights: Copyright © 2000 Tohoku University

JOURNAL ARTICLE
18 PAGES


SHARE
Vol.52 • No. 1 • 2000
Back to Top