Sharp spectral multipliers for Hardy spaces associated to non-negative self-adjoint operators
satisfying Davies–Gaffney estimates
Colloquium Mathematicum, Tome 133 (2013) no. 1, pp. 51-65
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We consider an abstract non-negative self-adjoint operator $L$ acting on $L^2(X)$ which satisfies Davies–Gaffney estimates. Let $H^p_L(X)$ $(p>0)$ be the Hardy spaces associated to the operator $L$. We assume that the doubling condition holds for the metric measure space $X$. We show that a sharp Hörmander-type spectral multiplier theorem on $H^p_L(X)$ follows from restriction-type estimates and Davies–Gaffney estimates. We also establish a sharp result for the boundedness of Bochner–Riesz means on $H^p_L(X)$.
Keywords:
consider abstract non negative self adjoint operator nbsp acting which satisfies davies gaffney estimates x hardy spaces associated operator nbsp assume doubling condition holds metric measure space sharp rmander type spectral multiplier theorem x follows restriction type estimates davies gaffney estimates establish sharp result boundedness bochner riesz means x
Affiliations des auteurs :
Peng Chen 1
@article{10_4064_cm133_1_4,
author = {Peng Chen},
title = {Sharp spectral multipliers for {Hardy} spaces associated to non-negative self-adjoint operators
satisfying {Davies{\textendash}Gaffney} estimates},
journal = {Colloquium Mathematicum},
pages = {51--65},
publisher = {mathdoc},
volume = {133},
number = {1},
year = {2013},
doi = {10.4064/cm133-1-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm133-1-4/}
}
TY - JOUR AU - Peng Chen TI - Sharp spectral multipliers for Hardy spaces associated to non-negative self-adjoint operators satisfying Davies–Gaffney estimates JO - Colloquium Mathematicum PY - 2013 SP - 51 EP - 65 VL - 133 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/cm133-1-4/ DO - 10.4064/cm133-1-4 LA - en ID - 10_4064_cm133_1_4 ER -
%0 Journal Article %A Peng Chen %T Sharp spectral multipliers for Hardy spaces associated to non-negative self-adjoint operators satisfying Davies–Gaffney estimates %J Colloquium Mathematicum %D 2013 %P 51-65 %V 133 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/cm133-1-4/ %R 10.4064/cm133-1-4 %G en %F 10_4064_cm133_1_4
Peng Chen. Sharp spectral multipliers for Hardy spaces associated to non-negative self-adjoint operators satisfying Davies–Gaffney estimates. Colloquium Mathematicum, Tome 133 (2013) no. 1, pp. 51-65. doi: 10.4064/cm133-1-4
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