Vector-valued extensions for fractional integrals of Laguerre expansions

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 expans...

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Detalhes bibliográficos
Autores: Ciaurri, Ó. [0000-0002-1695-3311], Roncal, L. [0000-0003-0852-3677]
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2018
País:España
Recursos:Universidad de La Rioja (UR)
Repositorio:RIUR. Repositorio Institucional de la Universidad de La Rioja
OAI Identifier:oai:portal.dialnet.es:doc/5bbc68f3b750603269e81253
Acesso em linha:https://investigacion.unirioja.es/documentos/5bbc68f3b750603269e81253
Access Level:acceso abierto
Palavra-chave:Fractional integral
Laguerre expansions
Mixed-norm spaces
Vector-valued inequalities
Weighted inequality
Descrição
Resumo: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.