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

Liliana Forzani, Roberto Scotto (1998)

Studia Mathematica

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 / d x 2 - 2 x d / d x , x ∈ ℝ, need not be of weak type (1,1). A function in L 1 ( d γ ) , 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.

Topologies on the group of invertible transformations

Maciej Burnecki, Robert Rałowski (2011)

Banach Center Publications

We enlarge the amount of embeddings of the group G of invertible transformations of [0,1] into spaces of bounded linear operators on Orlicz spaces. We show the equality of the inherited coarse topologies.

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