A maximal function on harmonic extensions of H-type groups
Annales mathématiques Blaise Pascal, Volume 13 (2006) no. 1, p. 87-101

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

@article{AMBP_2006__13_1_87_0,
     author = {Vallarino, Maria},
     title = {A maximal function on harmonic extensions of $H$-type groups},
     journal = {Annales math\'ematiques Blaise Pascal},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {13},
     number = {1},
     year = {2006},
     pages = {87-101},
     doi = {10.5802/ambp.214},
     mrnumber = {2233012},
     zbl = {1137.43003},
     language = {en},
     url = {http://www.numdam.org/item/AMBP_2006__13_1_87_0}
}
Vallarino, Maria. A maximal function on harmonic extensions of $H$-type groups. Annales mathématiques Blaise Pascal, Volume 13 (2006) no. 1, pp. 87-101. doi : 10.5802/ambp.214. http://www.numdam.org/item/AMBP_2006__13_1_87_0/

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