A maximal function on harmonic extensions of H -type groups

Maria Vallarino[1]

  • [1] Dipartimento di Matematica e Applicazioni Università di Milano-Bicocca Via R. Cozzi, 53 20125 Milano ITALY

Annales mathématiques Blaise Pascal (2006)

  • Volume: 13, Issue: 1, page 87-101
  • ISSN: 1259-1734

Abstract

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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 ) .

How to cite

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Vallarino, Maria. "A maximal function on harmonic extensions of $H$-type groups." Annales mathématiques Blaise Pascal 13.1 (2006): 87-101. <http://eudml.org/doc/10530>.

@article{Vallarino2006,
abstract = {Let $N$ be an $H$-type group and $S\simeq N\times \mathbb\{R\}^+$ be its harmonic extension. We study a left invariant Hardy–Littlewood maximal operator $M^\{\mathcal\{R\}\}_\{\rho \}$ on $S$, obtained by taking maximal averages with respect to the right Haar measure over left-translates of a family $\mathcal\{R\}$ of neighbourhoods of the identity. We prove that the maximal operator $M^\{\mathcal\{R\}\}_\{\rho \}$ is of weak type $(1,1)$.},
affiliation = {Dipartimento di Matematica e Applicazioni Università di Milano-Bicocca Via R. Cozzi, 53 20125 Milano ITALY},
author = {Vallarino, Maria},
journal = {Annales mathématiques Blaise Pascal},
keywords = {-type group; maximal function; weak type estimate},
language = {eng},
month = {1},
number = {1},
pages = {87-101},
publisher = {Annales mathématiques Blaise Pascal},
title = {A maximal function on harmonic extensions of $H$-type groups},
url = {http://eudml.org/doc/10530},
volume = {13},
year = {2006},
}

TY - JOUR
AU - Vallarino, Maria
TI - A maximal function on harmonic extensions of $H$-type groups
JO - Annales mathématiques Blaise Pascal
DA - 2006/1//
PB - Annales mathématiques Blaise Pascal
VL - 13
IS - 1
SP - 87
EP - 101
AB - Let $N$ be an $H$-type group and $S\simeq N\times \mathbb{R}^+$ be its harmonic extension. We study a left invariant Hardy–Littlewood maximal operator $M^{\mathcal{R}}_{\rho }$ on $S$, obtained by taking maximal averages with respect to the right Haar measure over left-translates of a family $\mathcal{R}$ of neighbourhoods of the identity. We prove that the maximal operator $M^{\mathcal{R}}_{\rho }$ is of weak type $(1,1)$.
LA - eng
KW - -type group; maximal function; weak type estimate
UR - http://eudml.org/doc/10530
ER -

References

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