香蕉视频

Title: Heat kernel bounds and desingularizing weights for non-local operators
Abstract: In 1998, Milman and Semenov introduced the method of desingularizing weights in order to obtain sharp two-sided bounds on the heat kernel of the Schroedinger operator with a potential having critical-order singularity at the origin. In this talk, I will discuss the method of desingularizing weights in a non-symmetric, non-local situation. In particular, I will talk about sharp two-sided bounds on the heat kernel of the fractional Laplacian perturbed by a Hardy drift. The crucial ingredient of the desingularization method is a weighted L^1->L^1 estimate on the semigroup, leading to the weighted Nash initial estimate. Milman and Semenov established this estimate appealing to the Stampacchia criterion in L^2. These arguments becomes quite problematic in the non-local non-symmetric situation (e.g. for a strong enough singularity of the drift, there is only L^p theory of the operator for p>2). The core of the talk will be the discussion of a new approach to the proof of this estimate. Joint with Yu.A.Semenov and K.Szczypkowsi (arxiv:1904.07363)