Heat kernel estimates of fractional Schrödinger operators with negative hardy potential

Abstract

We obtain two-sided estimates for the heat kernel (or the fundamental function) associated with the following fractional Schrödinger operator with negative Hardy potential $${\Delta }^{\alpha /2}-\lambda |x{|}^{-\alpha }$$ on $\RR^d$, where $\alpha \in (0,d\wedge 2)$ and $\lambda >0$. The proof is purely analytical but elementary. In particular, for upper bounds of heat kernel we use the Chapman-Kolmogorov equation and adopt self-improving argument.

26 pages

References in corpus (2)

• Factorization and estimates of Dirichlet heat kernels for non-local operators with critical killings
• The heat equation for the Dirichlet fractional Laplacian with Hardy's potentials: properties of minimal solutions and blow-up

Cited by in corpus (3)

• Equivalence of Sobolev norms involving generalized Hardy operators
• Subordinated Bessel heat kernels
• Two-sided weighted bounds on fundamental solution to fractional Schrödinger operator