Tohoku Mathematical Journal

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

Takeshi Kawazoe

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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

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

First available in Project Euclid: 3 May 2007

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Zentralblatt MATH identifier

Primary: 22E30: Analysis on real and complex Lie groups [See also 33C80, 43-XX]
Secondary: 42B25: Maximal functions, Littlewood-Paley theory 42B30: $H^p$-spaces 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)


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.

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