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 LP-norm inequalities for any p > 1 and a weak type Ll estimate. The aim of this paper is to find a subspace of L1 (G) from which they are bounded into L (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 L1 (G).
Original language | English |
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Pages (from-to) | 1-18 |
Number of pages | 18 |
Journal | Tohoku Mathematical Journal |
Volume | 52 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2000 |
Externally published | Yes |
ASJC Scopus subject areas
- Mathematics(all)