L1Estimates for Maximal Functions and Riesz Transform on Real Rank 1 Semisimple Lie Groups

Takeshi Kawazoe

研究成果: Article

3 引用 (Scopus)

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LetGbe a real rank one semisimple Lie group andKa maximal compact subgroup ofG. Radial maximal operators for suitable dilations, the heat and Poisson maximal operators, and the Riesz transform, which act onK-bi-invariant functions onG, satisfy theLp-norm inequalities forp 1 and a weak typeL1estimate. In this paper, through the Fourier theories onRandGwe shall duplicate the Hardy spaceH1(R) to a subspaceH1s(G) (s≥0) ofL1(G) and show that these operators are bounded fromH1s(G) toL1(G).

元の言語English
ページ(範囲)327-357
ページ数31
ジャーナルJournal of Functional Analysis
157
発行部数2
DOI
出版物ステータスPublished - 1998 8 20

ASJC Scopus subject areas

  • Analysis

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