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The higher order Riesz transform for Gaussian measure need not be of weak type (1,1)

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Forzani L., Scotto R.

Studia Mathematica

1998

tom 131

nr 3

205-214

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.

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1 Studia Mathematica

1 Forzani L.

1 Scotto R.

1 1998

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The higher order Riesz transform for Gaussian measure need not be of weak type (1,1)