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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 $L : = d^{2} / d x^{2} - 2 x d / d x$ , x ∈ ℝ, need not be of weak type (1,1). A function in $L^{1} (d γ)$ , 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.

The K-functional for rearrangement invariant spaces

Alberto Torchinsky (1979)

Studia Mathematica

The maximal normal subspace of the inverse image of a normal space of sequences by a non-negative matrix transformation

P. D. Johnson Jr., R. N. Mohapatra (1985)

Annales Polonici Mathematici

The numerical radius of a weighted shift operator with geometric weights.

Chien, Mao-Ting, Nakazato, Hiroshi (2009)

ELA. The Electronic Journal of Linear Algebra [electronic only]

The spectral decomposition of weighted shifts and the $A^{p}$ condition

Earl Berkson, T. A. Gillespie (1990)

Colloquium Mathematicae

The Szegö and Beurling theorems and operator factorizations

Lavon Page (1982)

Banach Center Publications

Théorie spectrale locale appliquée aux opérateurs shifts.

M. Houimdi, H. Zguitti (1999)

Extracta Mathematicae

Topological properties and matrix transformations of certain ordered generalized sequence spaces.

Gupta, Manjul, Kaushal, Kalika (1995)

International Journal of Mathematics and Mathematical Sciences

Topologies on the group of invertible transformations

Maciej Burnecki, Robert Rałowski (2011)

Banach Center Publications

We enlarge the amount of embeddings of the group G of invertible transformations of [0,1] into spaces of bounded linear operators on Orlicz spaces. We show the equality of the inherited coarse topologies.

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The behaviour of transformations on sequence spaces.

The Cauchy problem of the one dimensional Schrödinger equation with non-local potentials.

The curvature function and similarity of operators

The division method for subspectra of self-adjoint differential vector-operators.

The fine spectra discrete Cesàro operator on $b v_{0}$ .

The fine spectra of some Cesàro generalized operators defined on $ℓ^{p}$ ( $p > 1$ ).

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

The K-functional for rearrangement invariant spaces

The maximal normal subspace of the inverse image of a normal space of sequences by a non-negative matrix transformation

The numerical radius of a weighted shift operator with geometric weights.

The spectral decomposition of weighted shifts and the $A^{p}$ condition

The Szegö and Beurling theorems and operator factorizations

Théorie spectrale locale appliquée aux opérateurs shifts.

Topological properties and matrix transformations of certain ordered generalized sequence spaces.

Topologies on the group of invertible transformations

Transformaciones entre espacios de funciones continuas casi convergentes.

Translation invariant linear operators and generalized functions

Translation invariant subspaces of weighted l... and L... spaces.

Triangles which are bounded operators on $𝒜_{k}$ .

Currently displaying 1 – 19 of 19