Riesz transforms for the distinguished Laplacian on Damek–Ricci spaces and operator-valued multivariate spectral multipliers
Abstract
Let Δ = ∇ ∗ ∇ be the distinguished Laplacian on a Damek–Ricci space. We prove the L p -boundedness of the vector of first-order Riesz transforms ∇ Δ − 1 / 2 in the full range p ∈ ( 1 , ∞ ) . The most demanding part of the proof is establishing the boundedness for p ∈ ( 2 , ∞ ) ; this is obtained as a consequence of an operator-valued spectral multiplier theorem for the joint functional calculus of a commuting system of self-adjoint operators, which we prove here and may be of independent interest.
Fields of Study & Subjects
Advanced Harmonic Analysis Research
Mathematical Analysis and Transform Methods
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Journal of Functional Analysis
- Volume
- 292
- Issue
- 2
- Pages
- 111694–111694
- Publication date
- 30 September 2026
- Language
- EN