Heat Kernel Bounds for the Fractional Laplacian with Hardy Potential in Angular Momentum Channels
Abstract
Abstract Motivated by the study of relativistic atoms, we prove sharp heat kernel bounds for the Hardy operator $$(-\Delta )^{\alpha /2}-\kappa |x|^{-\alpha }$$ ( - Δ ) α / 2 - κ | x | - α acting on functions of the form $$u(|x|) |x|^{\ell } Y_{\ell ,m}(x/|x|)$$ u ( | x | ) | x | ℓ Y ℓ , m ( x / | x | ) in $$L^2(\mathbb {R}^d)$$ L 2 ( R d ) , when $$\alpha \in (0,2]\cap (0,d+2\ell )$$ α ∈ ( 0 , 2 ] ∩ ( 0 , d + 2 ℓ ) .
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Advanced Harmonic Analysis Research
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- Annales Henri Poincaré
- Publisher
- Springer Science and Business Media LLC
- Publication date
- 6 August 2026
- Language
- EN