Fractional operators with singular drift: smoothing properties and Morrey–Campanato spaces

Diego Chamorro ^[1] ; Stéphane Menozzi ^[1]
1. [1] University of Évry Val d'Essonne
  
  University of Évry Val d'Essonne
  
  Arrondissement d'Évry, Francia
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 32, Nº 4, 2016, págs. 1445-1499
Idioma: inglés
DOI: 10.4171/RMI/925
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Resumen
- We investigate some smoothness properties for a linear transport-diffusion equation involving a class of non-degenerate Lévy type operators with singular drift. Our main argument is based on a duality method using the molecular decomposition of Hardy spaces through which we derive some Hölder continuity for the associated parabolic PDE. This property will be fulfilled as far as the singular drift belongs to a suitable Morrey–Campanato space for which the regularizing properties of the Lévy operator suffice to obtain global Hölder continuity.