Fonctions maximales centrées de Hardy-Littlewood sur les groupes de Heisenberg

Hong-Quan Li

Hong-Quan Li

Studia Mathematica, Tome 192 (2009), p. 89-100 / Harvested from The Polish Digital Mathematics Library

Résumé

By getting uniformly asymptotic estimates for the Poisson kernel on Heisenberg groups $ℍ_{2 n + 1}$ , we prove that there exists a constant A > 0, independent of n ∈ ℕ*, such that for all $f \in L ¹ (ℍ_{2 n + 1})$ , we have ${| | M f | |}_{L^{1, \infty}} \leq A n | | f | | ₁$ , where M denotes the centered Hardy-Littlewood maximal function defined by the Carnot-Carathéodory distance or by the Korányi norm.

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:285304

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     title = {Fonctions maximales centr\'ees de Hardy-Littlewood sur les groupes de Heisenberg},
     journal = {Studia Mathematica},
     volume = {192},
     year = {2009},
     pages = {89-100},
     language = {fra},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm191-1-7}
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Hong-Quan Li. Fonctions maximales centrées de Hardy-Littlewood sur les groupes de Heisenberg. Studia Mathematica, Tome 192 (2009) pp. 89-100. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm191-1-7/