Annales Mathématiques
Blaise Pascal
no. 1
A maximal function on harmonic extensions of H-type groups
Maria Vallarino1
1 Dipartimento di Matematica e Applicazioni Università di Milano-Bicocca Via R. Cozzi, 53 20125 Milano ITALY
Annales mathématiques Blaise Pascal, Tome 13 (2006) no. 1, pp. 87-101.

Let N be an H-type group and S≃N×ℝ + be its harmonic extension. We study a left invariant Hardy–Littlewood maximal operator M ρ ℛ on S, obtained by taking maximal averages with respect to the right Haar measure over left-translates of a family ℛ of neighbourhoods of the identity. We prove that the maximal operator M ρ ℛ is of weak type (1,1).

DOI : 10.5802/ambp.214
Maria Vallarino 1

1 Dipartimento di Matematica e Applicazioni Università di Milano-Bicocca Via R. Cozzi, 53 20125 Milano ITALY 
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Maria Vallarino. A maximal function on harmonic extensions of $H$-type groups. Annales mathématiques Blaise Pascal, Tome 13 (2006) no. 1, pp. 87-101. doi : 10.5802/ambp.214. https://ambp.centre-mersenne.org/articles/10.5802/ambp.214/

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