Fractional operators with singular drift: smoothing properties and Morrey–Campanato spaces
Diego Chamorro
Université d'Évry Val d'Essonne, Evry, FranceStéphane Menozzi
Université d'Évry Val d'Essonne, Evry, France
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Abstract
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.
Cite this article
Diego Chamorro, Stéphane Menozzi, Fractional operators with singular drift: smoothing properties and Morrey–Campanato spaces. Rev. Mat. Iberoam. 32 (2016), no. 4, pp. 1445–1499
DOI 10.4171/RMI/925