The behaviour of transformations on sequence spaces.
The purpose of this paper is to prove that the higher order Riesz transform for Gaussian measure associated with the Ornstein-Uhlenbeck differential operator , x ∈ ℝ, need not be of weak type (1,1). A function in , 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.
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.