Spectral upper bound for the torsion function of symmetric stable processes

Hugo Panzo

Published 2020-01-14Version 1

We use H. Vogt's (2019) upper bound on the product of the principal eigenvalue and $L^\infty$ norm of the torsion function for Brownian motion killed upon exiting a domain in $\mathbb{R}^d$ to derive an analogous bound for the symmetric stable processes. In particular, the bound captures the correct order of growth in the dimension $d$, improving upon the existing result of Giorgi and Smits (2010). Along the way, we prove a torsion analogue of Chen and Song's (2005) two-sided eigenvalue estimates for subordinate Brownian motion, which may be of independent interest.