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

100%
Forzani L., Scotto R.
Studia Mathematica
|
1998
|
tom 131
|
nr 3
205-214
EN
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.
2
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Weighted weak type inequalities for certain maximal functions

100%
Aimar H., Forzani L.
Studia Mathematica
|
1991-1992
|
tom 101
|
nr 1
105-111
EN
We give an A_p type characterization for the pairs of weights (w,v) for which the maximal operator Mf(y) = sup 1/(b-a) ʃ_a^b |f(x)|dx, where the supremum is taken over all intervals [a,b] such that 0 ≤ a ≤ y ≤ b/ψ(b-a), is of weak type (p,p) with weights (w,v). Here ψ is a nonincreasing function such that ψ(0) = 1 and ψ(∞) = 0.
3
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On continuity properties of functions with conditions on the mean oscillation

100%
Aimar H., Forzani L.
Studia Mathematica
|
1993
|
tom 106
|
nr 2
139-151
EN
In this paper we study distribution and continuity properties of functions satisfying a vanishing mean oscillation property with a lag mapping on a space of homogeneous type.
4
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$L^{p}$ boundedness of Riesz transforms for orthogonal polynomials in a general context

81%
Forzani L., Sasso E., Scotto R.
Studia Mathematica
|
2015
|
tom 231
|
nr 1
45-71
EN
Nowak and Stempak (2006) proposed a unified approach to the theory of Riesz transforms and conjugacy in the setting of multi-dimensional orthogonal expansions, and proved their boundedness on L². Following them, we give easy to check sufficient conditions for their boundedness on $L^{p}$, 1 < p < ∞. We also discuss the symmetrized version of these transforms.
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