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<p>We obtain the boundedness of Hermite Riesz transforms of all orders on the Hermite Besov and Triebel–Lizorkin spaces for the full range of indices, completing an open problem. To achieve this, we develop a theory of almost diagonal operators for Hermite expansions.</p>

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Higher Order Riesz Transforms and Almost Diagonality for Hermite Expansions

  • 期刊论文

  • 发表日期：

    2025年12月12日

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  • The Anh Bui,
  • Fu Ken Ly

摘要

We obtain the boundedness of Hermite Riesz transforms of all orders on the Hermite Besov and Triebel–Lizorkin spaces for the full range of indices, completing an open problem. To achieve this, we develop a theory of almost diagonal operators for Hermite expansions.