Subcriticality and gaugeability for symmetric α-stable processes

An intrinsic necessary and sufficient condition for a measure being conditionally gaugeable was obtained in [Che2] and [T2]. We apply it to symmetric α-stable processes and give an interesting example of conditionally gaugeable measure. We show that for a Green-tight measure μ there exist constants θ^- and θ⁺ with θ^- < 0 < θ⁺ such that the operator -1/2(-Δ)^α/2 + θμ is subcritical if and only if θ belongs to the interval (θ^-, θ⁺).