Pointwise convergence of fractional powers of Hermite type operators
- Guillermo Flores 1
- Gustavo Garrigós 2
- Teresa Signes 2
- Beatriz Viviani 3
- 1 Universidad Nacional de Córdoba, Argentina
- 2 Universidad de Murcia, España
- 3 Universidad Nacional del Litoral, Argentina
ISSN: 1669-9637, 0041-6932
Année de publication: 2023
Volumen: 66
Número: 1
Pages: 187-205
Type: Article
D'autres publications dans: Revista de la Unión Matemática Argentina
Objectifs de Développement Durable
Résumé
When L is the Hermite or the Ornstein–Uhlenbeck operator, we find minimal integrability and smoothness conditions on a function f so that the fractional power Lσf(x0) is well-defined at a given point x0. We illustrate the optimality of the conditions with various examples. Finally, we obtain similar results for the fractional operators (−∆ + R) σ, with R > 0.