Vector-valued extensions for fractional integrals of Laguerre expansions

Abstract

We prove some vector-valued inequalities for fractional integrals defined in the context of two different orthonormal systems of Laguerre functions. Our results are based on estimates of the corresponding kernels with precise control of the parameters involved. As an application, mixed norm estimates for the fractional integrals related to the harmonic oscillator are deduced.

21 pages. Revised version

References in corpus (2)

• Negative powers of Laguerre operators
• Potential operators associated with Jacobi and Fourier-Bessel expansions

Cited by in corpus (6)

• The Riesz transform for the harmonic oscillator in spherical coordinates
• Sharp estimates for potential operators associated with Laguerre and Dunkl-Laguerre expansions
• Revisiting Riesz transforms for Hermite and Special Hermite Operators
• Hardy-type inequalities for fractional powers of the Dunkl--Hermite operator
• Mixed norm estimates for Hermite multipliers
• Riesz transforms on compact Riemannian symmetric spaces of rank one