Vector-valued extensions for fractional integrals of Laguerre expansions
  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. 
\'O. Ciaurri, L. Roncal
math.CA math.FA