Geodesic
The higher order Riesz transform for Gaussian measure need not be of weak type (1,1)
Studia Mathematica, Tome 131 (1998) no. 3, pp. 205-214

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The purpose of this paper is to prove that the higher order Riesz transform for Gaussian measure associated with the Ornstein-Uhlenbeck differential operator $L:= d^2/dx^2 - 2xd/dx$, x ∈ ℝ, need not be of weak type (1,1). A function in $L^1(dγ)$, where dγ is the Gaussian measure, is given such that the distribution function of the higher order Riesz transform decays more slowly than C/λ.
DOI : 10.4064/sm-131-3-205-214
Keywords: Fourier analysis, Gaussian measure, Poisson-Hermite integrals, Hermite expansions

Liliana Forzani 1 ;  1

1 
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Liliana Forzani;  . The higher order Riesz transform for Gaussian measure need not be of weak type (1,1). Studia Mathematica, Tome 131 (1998) no. 3, pp. 205-214. doi: 10.4064/sm-131-3-205-214

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