The boundedness of Riesz 𝑠-transforms of measures in ℝⁿ

DOI10.1090/S0002-9939-96-03522-8zbMath0876.28008MaRDI QIDQ3837620

Merja Vihtilä

Publication date: 10 December 1996

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Borel measuresRadon measuresRiesz transformtangent measures\(L^ 2\)-boundedness

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Length, area, volume, other geometric measure theory (28A75)

Related Items (13)

Calderón-Zygmund capacities and Wolff potentials on Cantor sets ⋮ Principal values for the signed Riesz kernels of non-integer dimension ⋮ Calderón-Zygmund kernels and rectifiability in the plane ⋮ Mass transport and uniform rectifiability ⋮ On the Maximum Principle for the Riesz Transform ⋮ Reflectionless measures for Calderón-Zygmund operators. II: Wolff potentials and rectifiability ⋮ The Riesz Transform of Codimension Smaller Than One and the Wolff Energy ⋮ The measures with an associated square function operator bounded in \(L^2\) ⋮ Singular Integrals on Self-similar Subsets of Metric Groups ⋮ Riesz transforms of non-integer homogeneity on uniformly disconnected sets ⋮ The \(s\)-Riesz transform of an \(s\)-dimensional measure in \(\mathbb R^2\) is unbounded for \(1<s<2\) ⋮ Finite square function implies integer dimension ⋮ The fractional Riesz transform and an exponential potential

Cites Work

• Geometry of measures in \(R^ n:\) Distribution, rectifiability, and densities
• Rectifiable Measures in R ⁿ and Existence of Principal Values for Singular Integrals
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