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$L^p $ boundedness of Riesz transforms for orthogonal polynomials in a general context

Volume 231 / 2015

Liliana Forzani, Emanuela Sasso, Roberto Scotto Studia Mathematica 231 (2015), 45-71 MSC: 42C05, 42C15. DOI: 10.4064/sm8221-1-2016 Published online: 10 February 2016

Abstract

Nowak and Stempak (2006) proposed a unified approach to the theory of Riesz transforms and conjugacy in the setting of multi-dimensional orthogonal expansions, and proved their boundedness on $L^2$. Following them, we give easy to check sufficient conditions for their boundedness on $L^p$, $1 \lt p \lt \infty $. We also discuss the symmetrized version of these transforms.

Authors

  • Liliana ForzaniDepartamento de Matemática
    Facultad de Ingeniería Química (UNL)
    Instituto de Matemática Aplicada del Litoral - IMAL (CONICET-UNL) 3000 Santa Fe, Argentina
    e-mail
  • Emanuela SassoDipartimento di Matematica
    Università di Genova
    Genova, Italy
    e-mail
  • Roberto ScottoDepartamento de Matemática
    Facultad de Ingeniería Química (UNL)
    Instituto de Matemática Aplicada del Litoral - IMAL (CONICET-UNL) 3000 Santa Fe, Argentina
    e-mail

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