Sharp spectral multipliers for Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates

Peng Chen. "Sharp spectral multipliers for Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates." Colloquium Mathematicae 133.1 (2013): 51-65. <http://eudml.org/doc/286325>.

@article{PengChen2013,
abstract = {We consider an abstract non-negative self-adjoint operator L acting on L²(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 $H^\{p\}_\{L\}(X)$.},
author = {Peng Chen},
journal = {Colloquium Mathematicae},
keywords = {Hardy spaces; spectral multipliers; non-negative self-adjoint operator; Davies-Gaffney estimates; restriction type estimate; Bochner-Riesz means; metric measure space},
language = {eng},
number = {1},
pages = {51-65},
title = {Sharp spectral multipliers for Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates},
url = {http://eudml.org/doc/286325},
volume = {133},
year = {2013},
}

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 Mathematicae
PY - 2013
VL - 133
IS - 1
SP - 51
EP - 65
AB - We consider an abstract non-negative self-adjoint operator L acting on L²(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 $H^{p}_{L}(X)$.
LA - eng
KW - Hardy spaces; spectral multipliers; non-negative self-adjoint operator; Davies-Gaffney estimates; restriction type estimate; Bochner-Riesz means; metric measure space
UR - http://eudml.org/doc/286325
ER -