Vector-valued extensions for fractional integrals of Laguerre expansions

  1. Ciaurri, Ó. 2
  2. Roncal, L. 12
  1. 1 Basque Center for Applied Mathematics
    info

    Basque Center for Applied Mathematics

    Bilbao, España

    ROR 03b21sh32

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Studia Mathematica

ISSN: 0039-3223

Año de publicación: 2018

Volumen: 240

Número: 1

Páginas: 69-99

Tipo: Artículo

DOI: 10.4064/SM8675-2-2017 SCOPUS: 2-s2.0-85044337784 WoS: WOS:000418492400004 GOOGLE SCHOLAR

Otras publicaciones en: Studia Mathematica

Repositorio institucional: lockAcceso abierto Editor

Proyectos relacionados

Ortogonalidad, teoría de la aproximación y aplicaciones en física matemática.

2016/00008/001

Resumen

We prove some vector-valued inequalities for fractional integrals defined for several orthonormal systems of Laguerre functions. On the one hand, we obtain weighted Lp-Lq 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 Lp-Lq 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. © Instytut Matematyczny PAN, 2018.