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• W2055681526 abstract "In this paper we develop a theory of singular integral operators acting on function spaces over the measured metric space (Rd,ρ,γ), where ρ denotes the Euclidean distance and γ the Gauss measure. Our theory plays for the Ornstein–Uhlenbeck operator the same rôle that the classical Calderòn–Zygmund theory plays for the Laplacian on (Rd,ρ,λ), where λ is the Lebesgue measure. Our method requires the introduction of two new function spaces: the space BMO(γ) of functions with “bounded mean oscillation” and its predual, the atomic Hardy space H1(γ). We show that if p is in (2,∞), then Lp(γ) is an intermediate space between L2(γ) and BMO(γ), and that an inequality of John–Nirenberg type holds for functions in BMO(γ). Then we show that if M is a bounded operator on L2(γ) and the Schwartz kernels of M and of its adjoint satisfy a “local integral condition of Hörmander type,” then M extends to a bounded operator from H1(γ) to L1(γ), from L∞(γ) to BMO(γ) and on Lp(γ) for all p in (1,∞). As an application, we show that certain singular integral operators related to the Ornstein–Uhlenbeck operator, which are unbounded on L1(γ) and on L∞(γ), turn out to be bounded from H1(γ) to L1(γ) and from L∞(γ) to BMO(γ)." @default.
• W2055681526 created "2016-06-24" @default.
• W2055681526 creator A5038991948 @default.
• W2055681526 creator A5078436419 @default.
• W2055681526 date "2007-11-01" @default.
• W2055681526 modified "2023-09-24" @default.
• W2055681526 title "BMO and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:msup><mml:mi>H</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:math> for the Ornstein–Uhlenbeck operator" @default.
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• W2055681526 doi "https://doi.org/10.1016/j.jfa.2007.06.017" @default.
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