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
Cet article a éte moissonné depuis 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.
Keywords:
Fourier analysis, Gaussian measure, Poisson-Hermite integrals, Hermite expansions
@article{10_4064_sm_131_3_205_214,
author = {Liliana Forzani and },
title = {The higher order {Riesz} transform for {Gaussian} measure need not be of weak type (1,1)},
journal = {Studia Mathematica},
pages = {205--214},
year = {1998},
volume = {131},
number = {3},
doi = {10.4064/sm-131-3-205-214},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-131-3-205-214/}
}
TY - JOUR AU - Liliana Forzani AU - TI - The higher order Riesz transform for Gaussian measure need not be of weak type (1,1) JO - Studia Mathematica PY - 1998 SP - 205 EP - 214 VL - 131 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4064/sm-131-3-205-214/ DO - 10.4064/sm-131-3-205-214 LA - en ID - 10_4064_sm_131_3_205_214 ER -
%0 Journal Article %A Liliana Forzani %A %T The higher order Riesz transform for Gaussian measure need not be of weak type (1,1) %J Studia Mathematica %D 1998 %P 205-214 %V 131 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4064/sm-131-3-205-214/ %R 10.4064/sm-131-3-205-214 %G en %F 10_4064_sm_131_3_205_214
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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