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
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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