Endpoint estimates for higher-order Gaussian Riesz Transforms

• Fabio Berra ^[1] ; Estefanía Dalmasso ^[2] ; Roberto Scotto ^[1]
  1. [1] Universidad Nacional del Litoral,Santa Fe, Argentina
  2. [2] Instituto de Matem´atica Aplicada del Litoral, Santa Fe, Argentina
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 69, Nº. 1, 2026, págs. 25-43
• Idioma: inglés
• DOI: 10.33044/revuma.4878
• Enlaces
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• Resumen

  • We show that, contrary to the behavior of the higher-order Riesz transforms studied so far on the atomic Hardy space H1(Rn, γ) associated with the Ornstein–Uhlenbeck operator with respect to the n-dimensional Gaussian measure γ, the new Gaussian Riesz transforms are bounded from H1 (Rn, γ) toL1(Rn, γ), for any order and any dimension n. We also prove that the classical Gaussian Riesz transforms of higher order are bounded from an appropriate subspace of H1(Rn, γ) into L1(Rn, γ), extending T. Bruno (2019) to the firstorder case.

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