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

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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 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 languageEnglish
Pages (from-to)1-18
Number of pages18
JournalTohoku Mathematical Journal
Issue number1
Publication statusPublished - 2000 Jan 1


ASJC Scopus subject areas

  • Mathematics(all)

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