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

• Autorzy: Peng Chen
• Języki publikacji: EN

Abstrakty

EN

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 $H^{p}_{L}(X)$.

Kategorie tematyczne

• 42B15: Multipliers
• 47F05: Partial differential operators (should also be assigned at least one other classification number in section 47)
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)
• 42B30: H p -spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 133
• Numer: 1
• Strony: 51-65

Daty

wydano

2013

Twórcy

autor

Peng Chen

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

Identyfikatory

DOI

10.4064/cm133-1-4