Calderón-Zygmund operators and endpoint spaces for Hermite expansions

2023/09/07 by The Anh Bui, Bui, The Anh, Fu Ken Ly +1
Mathematics · #33C45 #42B20 #42B30 #42B35 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2309.03424

openalex publication_date 2023/09/07 · openalex created_date 2023/09/09 · openalex updated_date 2026/07/28

Abstract

Let L=-Δ+|x|² be the Hermite operator on ℝⁿ, and T be a Calderón-Zygmund type operator that is modelled on certain singular integrals related to L. We establish necessary and sufficient conditions for T to be bounded on various function spaces including the Hardy spaces and the Lipschitz spaces associated to L. We then apply our results to study the boundedness of the Riesz transforms and pseudo-multipliers associated to L.

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