Feller Generators with Measure-valued Drifts

We construct a L ^p -strong Feller process associated with the formal differential operator ? Δ + σ ?? on (mathbb R^{d}), (d geqslant 3), with drift σ in a wide class of measures (e.g. the sum of a measure having density in weak L ^d space and a Kato class measure), by exploiting a quantitative dependence of the smoothness of the domain of an operator realization of ? Δ + σ ?? generating a holomorphic C ₀-semigroup on (L^{p}(mathbb R^{d})), p > d ? 1, on the value of the relative bound of σ.