Second-order subelliptic operators on Lie groups. III: Hölder continuous coefficients
[Parts I and II by the same authors in Acta Appl. Math. 59, 299-331 (1999; see the preceding review) and Prog. Nonlin. Differential Equations Appl. 42, 103-142 (Basel 2000), respectively.] The paper is devoted to the study of relations between the smoothness properties of the coefficients of second-order subelliptic operators \(H\) on a connected Lie group \(G\) with smoothness of the associated semigroup kernel. The principal coefficients of the operator \(H\) are assumed to be Hölder continuous for \(H\) written in divergence form and at least once differentiable otherwise. It is established that the semigroup kernel is almost one degree more differentiable than the coefficients, and the kernel and its derivatives satisfy Gaussian bounds. If the operator \(H\) is in nondivergence form the improvement in smoothness is almost two degrees, and the Gaussian bounds are still valid.
Fredholm and Volterra integral equations
scientific article; zbMATH DE number 1333048