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

Peng Chen¹

¹ School of Information Technology and Mathematical Sciences University of South Australia Adelaide, SA, 5095, Australia

Colloquium Mathematicum, Tome 133 (2013) no. 1, pp. 51-65.

Résumé

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 $H^p_L(X)$.

Détail

DOI : 10.4064/cm133-1-4

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