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.

10 pages, 1 figure; v2 (corrections in Section 3 concerning Theorem 3.1 and its proof and Figure 1)

References in corpus (1)

• Negative powers of Laguerre operators

Cited by in corpus (4)

• Potential operators associated with Jacobi and Fourier-Bessel expansions
• Sharp estimates for potential operators associated with Laguerre and Dunkl-Laguerre expansions
• Potential operators associated with Hankel and Hankel-Dunkl transforms
• Unique continuation for the heat operator with potentials in weak spaces