Fractional Leibniz-type Rules on Spaces of Homogeneous Type

Let (M,ρ,μ) be a space of homogeneous type satisfying the reverse doubling condition and the non-collapsing condition. In view of the lack of the Fourier transform in this setting, the authors obtain Leibniz-type rules of fractional order on (M,ρ,μ) under the assumptions of the heat kernel satisfying the upper bound estimate, the Hölder estimate and the stochastic completeness property.