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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

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.

$L^{p}$ 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

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.

Ograniczanie wyników

2 Studia Mathematica

2 Forzani L.

2 Scotto R.

1 Sasso E.

1 2015

1 1998

Wyniki wyszukiwania

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

$L^{p}$ boundedness of Riesz transforms for orthogonal polynomials in a general context