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

DOI10.4064/CM8047-8-2020zbMath1467.42044arXiv1909.11153OpenAlexW3115496755MaRDI QIDQ4997556

MacIej Kucharski

Publication date: 29 June 2021

Published in: Colloquium Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.11153

zbMATH Keywords

Bellman functionRiesz transformHermite expansions

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Conjugate functions, conjugate series, singular integrals (42A50) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50)

Related Items (2)

Trilinear embedding for divergence-form operators with complex coefficients ⋮ Dimension-free \(L^p\)-estimates for vectors of Riesz transforms in the rational Dunkl setting

Uses Software

• DLMF

Cites Work

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• Functional calculus for generators of symmetric contraction semigroups
• Bilinear embedding for real elliptic differential operators in divergence form with potentials
• Riesz transforms and spectral multipliers of the Hodge-Laguerre operator
• Dimension free estimates for Riesz transforms associated to the harmonic oscillator on \(\mathbb R^n\)
• \(L^2\)-theory of Riesz transforms for orthogonal expansions
• \(L^p\)-dimension free boundedness for Riesz transforms associated to Hermite functions
• Dimension-free \(L^p\) estimates for vectors of Riesz transforms associated with orthogonal expansions
• Bellman function and linear dimension-free estimates in a theorem of Bakry
• Schrödinger operators with singular potentials
• Linear dimension-free estimates in the embedding theorem for Schrödinger operators
• Some results in harmonic analysis in 𝐑ⁿ, for 𝐧→∞

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