Two bounds for the X-ray transform

DOI10.1007/s00209-009-0589-5zbMath1269.42013arXivmath/0610942OpenAlexW1988604961MaRDI QIDQ707566

Richard Oberlin

Publication date: 8 October 2010

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0610942

zbMATH Keywords

X-ray transformRadonKakeya maximal operator

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25)

Related Items (4)

Integrability of orthogonal projections, and applications to Furstenberg sets ⋮ On the Fourier dimension of \((d, k)\)-sets and Kakeya sets with restricted directions ⋮ Norm estimates for \(k\)-plane transforms and geometric inequalities ⋮ Hausdorff Dimension, Projections, Intersections, and Besicovitch Sets

Cites Work

• Unnamed Item
• \(L^p\) estimates for the X-ray transform
• Besicovitch type maximal operators and applications to Fourier analysis
• A mixed norm estimate for the \(X\)-ray transform
• On the dimension of Kakeya sets and related maximal inequalities
• Bounds on arithmetic projections, and applications to the Kakeya conjecture
• New bounds for Kakeya problems
• An improved bound for Kakeya type maximal functions
• The Bochner-Riesz conjecture implies the restriction conjecture
• Continuity properties of k-plane integrals and Besicovitch sets
• Packing planes in ℝ ³
• 𝐿^{𝑝} improving bounds for averages along curves
• An X-ray transform estimate in \(\mathbb R^n\)

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