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Dimension-free estimates for Riesz transforms related to the harmonic oscillator

Volume 165 / 2021

Maciej Kucharski Colloquium Mathematicum 165 (2021), 139-161 MSC: 42C10, 42A50, 33C50. DOI: 10.4064/cm8047-8-2020 Published online: 19 December 2020

Abstract

We study bounds for two kinds of Riesz transforms on \mathbb R ^d related to the harmonic oscillator. We pursue an explicit estimate of their L^p norms that is independent of the dimension d and linear in \max (p, p/(p-1)).

Authors

  • Maciej KucharskiInstitute of Mathematics
    University of Wrocław
    pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
    e-mail

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