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      https://www.ias.ac.in/article/fulltext/pmsc/119/02/0203-0220

    • Keywords

       

      Laguerre functions.

    • Abstract

       

      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.

    • Author Affiliations

       

      I Abu-Falahah1 R A Macías2 C Segovia3 J L Torrea1

      1. Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain
      2. IMAL-FIQ, Universidad Nacional del Litoral, Güemes 3450, 3000 Santa Fe, Argentina
      3. Carlos Segovia passed away on April 3, 2007
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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