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Weak Type Inequality for a Family of Singular Integral Operators Related with the Gaussian Measure

Authors:	Liliana Forzani Eleonor Harboure Roberto Scotto

Institution:	(1) Departamento de Matemática and Instituto de Matemática del Litoral, CONICET, Universidad Nacional del Litoral, Santa Fe, 3000, Argentina

Abstract:	In this paper we study a family of singular integral operators that generalizes the higher order Gaussian Riesz Transforms and find the right weight w to make them continuous from L ¹(wdγ) into L ^1, ∞(dγ), being $d\gamma(x)=e^{-\|x\|^2}dx.$ Some boundedness properties of these operators had already been derived by Urbina (Ann Scuola Norm Sup Pisa Cl Sci 17(4):531–567, 1990) and Pérez (J Geom Anal 11(3):491–507, 2001).

Keywords:	Ornstein-Uhlenbeck operator Functional calculus Gaussian measure Singular integrals
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