TY - JOUR
T1 - Hardy spaces and maximal operators on real rank one semisimple lie groups I
AU - Kawazoe, Takeshi
PY - 2000/1/1
Y1 - 2000/1/1
N2 - 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).
AB - 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).
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U2 - 10.2748/tmj/1178224654
DO - 10.2748/tmj/1178224654
M3 - Article
AN - SCOPUS:0034343756
VL - 52
SP - 1
EP - 18
JO - Tohoku Mathematical Journal
JF - Tohoku Mathematical Journal
SN - 0040-8735
IS - 1
ER -