Displaying similar documents to “On summability of measures with thin spectra”

A microlocal F. and M. Riesz theorem with applications.

Raymondus G. M. Brummelhuis (1989)

Revista Matemática Iberoamericana

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Consider, by way of example, the following F. and M. Riesz theorem for R: Let μ be a finite measure on R whose Fourier transform μ* is supported in a closed convex cone which is proper, that is, which contains no entire line. Then μ is absolutely continuous (cf. Stein and Weiss [SW]). Here, as in the sequel, absolutely continuous means with respect to Lebesque measure. In this theorem one can replace the condition on the support of μ* by a similar condition on the wave front set WF(μ)...

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.

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 ⨍ ∈ 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 ⨍ ∈ H p ( ℝ ) , the Riesz...