The higher order Riesz transform for Gaussian measure need not be of weak type (1,1)
Forzani, Liliana ; Scotto, Roberto
Studia Mathematica, Tome 129 (1998), p. 205-214 / Harvested from The Polish Digital Mathematics Library
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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:=d2/dx2-2xd/dx, x ∈ ℝ, need not be of weak type (1,1). A function in L1(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.

Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:216576 
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     title = {The higher order Riesz transform for Gaussian measure need not be of weak type (1,1)},
     journal = {Studia Mathematica},
     volume = {129},
     year = {1998},
     pages = {205-214},
     zbl = {0954.42009},
     language = {en},
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Forzani, Liliana; Scotto, Roberto. The higher order Riesz transform for Gaussian measure need not be of weak type (1,1). Studia Mathematica, Tome 129 (1998) pp. 205-214. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv131i3p205bwm/

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