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We investigate some smoothness properties for a transport-diffusion equationinvolving a class of non-degerate L{\'e}vy type operators with singular drift.Our main argument is based on a duality method using the moleculardecomposition of Hardy spaces through which we derive some H{\"o}ldercontinuity for the associated parabolic PDE. This property will be fulfilled asfar as the singular drift belongs to a suitable Morrey-Campanato space forwhich the regularizing properties of the L{\'e}vy operator suffice to obtainglobal H{\"o}lder continuity.

Fractional operators with singular drift: Smoothing properties and Morrey-Campanato spaces