Sharp estimates of the potential kernel for the harmonic oscillator with applications

Abstract

We prove qualitatively sharp estimates of the potential kernel for the harmonic oscillator. These bounds are then used to show that the $L^p-L^q$ estimates of the associated potential operator obtained recently by Bongioanni and Torrea are in fact sharp.Comment: 10 pages, 1 figure; v2 (corrections in Section 3 concerning Theorem 3.1 and its proof and Figure 1