Pointwise convergence of fractional powers of Hermite type operators

Guillermo Flores ^[1] ; Gustavo Garrigós ^[2] ; Teresa Signes ^[2] ; Beatriz Viviani ^[3]
1. [1] Universidad Nacional de Córdoba
  
  Universidad Nacional de Córdoba
  
  Argentina
2. [2] Universidad de Murcia
  
  Universidad de Murcia
  
  Murcia, España
3. [3] Universidad Nacional del Litoral
  
  Universidad Nacional del Litoral
  
  Argentina
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Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 66, Nº. 1, 2023, págs. 187-205
Idioma: inglés
DOI: 10.33044/revuma.4357
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Resumen
- 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.