Transferring Strong Boundedness among Laguerre Orthogonal Systems

Proceedings Mathematical Sciences

J L Torrea¹  R A Macías³  C Segovia²  I Abu-Falahah⁴ 

[1] $$;Carlos Segovia passed away on April , 00$$;IMAL-FIQ, Universidad Nacional del Litoral, Güemes 0, 000 Santa Fe, Argentina$$;Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 0 Madrid, Spain$$

关键词: Laguerre functions.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Given the family of Laguerre polynomials, it is known that several orthonormal systems of Laguerre functions can be considered. In this paper we prove that an exhaustive knowledge of the boundedness in weighted $L^p$ of the heat and Poisson semigroups, Riesz transforms and 𝑔-functions associated to a particular Laguerre orthonormal system of functions, implies a complete knowledge of the boundedness of the corresponding operators on the other Laguerre orthonormal system of functions. As a byproduct, new weighted $L^p$ boundedness are obtained. The method also allows us to get new weighted estimates for operators related with Laguerre polynomials.

【 授权许可】

Unknown