4:00pm – Tomasz Jakubowski
Title: Fractional Laplacian with singular drift.
Abstract: We consider the fractional Laplacian perturbed by the gradient operator b(x)nabla for various classes of vector fields b. We construct end estimate the corresponding semigroup.
4:30pm – Karol Szczypkowski
Title: Gradient and Schrödinger perturbations of transition densities
Abstract: We consider time-space integrability conditions on a drift term (for gradient pert.) and a potential (for Schrödinger pert.) under which we obtain certain estimates of the perturbations of general transition densities.
We prove an optimal 4G Theorem for the Gaussian kernel, the inequality which is a non- trivial extension of the so called 3G Theorem ([2], [1]) and a counterpart of the 3P Theorem ([3], [4]) (as well known, 3P fails in its primary form for the Gaussian kernel). Furthermore, a new method of estimating Schrödinger perturbations applies to the Gaussian kernel.