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Vector-valued extensions for fractional integrals of Laguerre expansions

Volume 240 / 2018

Óscar Ciaurri, Luz Roncal Studia Mathematica 240 (2018), 69-99 MSC: Primary 42C10; Secondary 47G40, 26A33, 42B35, 33C45. DOI: 10.4064/sm8675-2-2017 Published online: 6 July 2017

Abstract

We prove some vector-valued inequalities for fractional integrals defined for several orthonormal systems of Laguerre functions. On the one hand, we obtain weighted $L^p$-$L^q$ vector-valued extensions, in a multidimensional setting, for negative powers of the operator related to so-called Laguerre expansions of Hermite type. On the other hand, we give necessary and sufficient conditions for vector-valued $L^p$-$L^q$ estimates related to negative powers of the Laguerre operator associated to expansions of convolution type, in a one-dimensional setting. Both types of vector-valued inequalities are based on estimates of the kernel with precise control of the parameters involved. As an application, mixed norm estimates for fractional integrals related to the harmonic oscillator are deduced.

Authors

  • Óscar Ciaurri
  • Luz Roncal

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