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

Liliana Forzani; Roberto Scotto

Displaying similar documents to “The higher order Riesz transform for Gaussian measure need not be of weak type (1,1)”

Weak-type estimates for the Riesz transforms associated with the Gaussian measure.

Eugene B. Fabes, Chritian E. Gutiérrez, Roberto Scotto (1994)

Revista Matemática Iberoamericana

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In this paper we will study the behavior of the Riesz transform associated with the Gaussian measure γ(x)dx = edx in the space L (R).

Riesz means of Fourier transforms and Fourier series on Hardy spaces

Ferenc Weisz (1998)

Studia Mathematica

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Elementary estimates for the Riesz kernel and for its derivative are given. Using these we show that the maximal operator of the Riesz means of a tempered distribution is bounded from $H_{p} (ℝ)$ to $L_{p} (ℝ)$ (1/(α+1) < p < ∞) and is of weak type (1,1), where $H_{p} (ℝ)$ is the classical Hardy space. As a consequence we deduce that the Riesz means of a function $⨍ \in L_{1} (ℝ)$ converge a.e. to ⨍. Moreover, we prove that the Riesz means are uniformly bounded on $H_{p} (ℝ)$ whenever 1/(α+1) < p < ∞. Thus, in case $⨍ \in H_{p} (ℝ)$ , the Riesz...

The size of some classes of thin sets

Russell Lyons (1987)

Studia Mathematica

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Some properties of Holmgren-Riesz transform in two dimensions

M. A. Bassam (1962)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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On conjugate Poisson integrals and Riesz transforms for the Hermite expansions

S. Thangavelu (1993)

Colloquium Mathematicae

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On Riesz product measures ; mutual absolute continuity and singularity

Shelby J. Kilmer, Sadahiro Saeki (1988)

Annales de l'institut Fourier

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We give some criteria for mutual absolute continuity and for singularity of Riesz product measures on locally compact abelian groups. The first section gives the definition of such a measure which is more general than the usual definition. The second section provides three sufficient conditions for one Riesz product measure to be absolutely continuous with respect to another. One of our results contains a theorem of Brown-Moran-Ritter as a special case. The final section deals with random...

Henkin measures, Riesz products and singular sets

Evgueni Doubtsov (1998)

Annales de l'institut Fourier

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The mutual singularity problem for measures with restrictions on the spectrum is studied. The $d$ -pluriharmonic Riesz product construction on the complex sphere is introduced. Singular pluriharmonic measures supported by sets of maximal Hausdorff dimension are obtained.