Hardy spaces and maximal operators on real rank 1 semisimple Lie groups I
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概要
- 論文の詳細を見る
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 $L^1(G)$.
- 東北大学の論文
- 2000-03-00
著者
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Kawazoe Takeshi
Department Of Mathematics Faculty Of Science And Technology Keio University
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Kawazoe Takeshi
Department of Mathematics, Keio University at Fujisawa
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