On étudie la croissance des fonctions harmoniques sur les variétés riemanniennes complètes dont le diamètre des grandes sphères géodésiques croît sous linéairement. Il s’agit d’une généralisation de travaux de A. Kasue. Nous obtenons aussi un résultat de continuité pour la transformée de Riesz
We study the growth of harmonic functions on complete Riemannian manifolds where the extrinsic diameter of geodesic spheres is sublinear. It is an generalization of a result of A. Kasue. Our estimates also yields a result on the boundedness of the Riesz transform.
Mots clés : Inégalités de Poincaré, fonctions harmoniques, transformée de Riesz.
@article{AMBP_2016__23_2_249_0,
author = {Carron, Gilles},
title = {Harmonic functions on {Manifolds} whose large spheres are small.},
journal = {Annales math\'ematiques Blaise Pascal},
pages = {249--261},
publisher = {Annales math\'ematiques Blaise Pascal},
volume = {23},
number = {2},
year = {2016},
doi = {10.5802/ambp.362},
language = {en},
url = {http://www.numdam.org/articles/10.5802/ambp.362/}
}
TY - JOUR AU - Carron, Gilles TI - Harmonic functions on Manifolds whose large spheres are small. JO - Annales mathématiques Blaise Pascal PY - 2016 SP - 249 EP - 261 VL - 23 IS - 2 PB - Annales mathématiques Blaise Pascal UR - http://www.numdam.org/articles/10.5802/ambp.362/ DO - 10.5802/ambp.362 LA - en ID - AMBP_2016__23_2_249_0 ER -
%0 Journal Article %A Carron, Gilles %T Harmonic functions on Manifolds whose large spheres are small. %J Annales mathématiques Blaise Pascal %D 2016 %P 249-261 %V 23 %N 2 %I Annales mathématiques Blaise Pascal %U http://www.numdam.org/articles/10.5802/ambp.362/ %R 10.5802/ambp.362 %G en %F AMBP_2016__23_2_249_0
Carron, Gilles. Harmonic functions on Manifolds whose large spheres are small.. Annales mathématiques Blaise Pascal, Tome 23 (2016) no. 2, pp. 249-261. doi : 10.5802/ambp.362. http://www.numdam.org/articles/10.5802/ambp.362/
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