Mixed norm estimates for a restricted X-ray transform.

DOI10.1007/BF02868473zbMath1037.42019MaRDI QIDQ1809911

Michael Christ, Mehmet Burak Erdogan

Publication date: 2002

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

zbMATH Keywords

X-ray transformrestricted weak-type estimateshairbrush argument

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Radon transform (44A12)

Related Items (10)

Universal \(L^p\) improving for averages along polynomial curves in low dimensions ⋮ Loomis-Whitney inequalities in Heisenberg groups ⋮ 𝐿^{𝑝} improving bounds for averages along curves ⋮ Uniform \(L_x^p - L_{x, r}^q\) improving for dilated averages over polynomial curves ⋮ Uniform estimates for the X-ray transform restricted to polynomial curves ⋮ Mixed norm estimates for certain generalized Radon transforms ⋮ Estimates for the \(X\)-ray transform restricted to 2-manifolds ⋮ A note on restricted X-ray transforms ⋮ Existence of extremizers for a model convolution operator ⋮ 𝐿^{𝑝}-𝐿^{𝑝’} estimates for overdetermined Radon transforms

Cites Work

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• Besicovitch type maximal operators and applications to Fourier analysis
• A mixed norm estimate for the \(X\)-ray transform
• A sharp bilinear cone restriction estimate
• An improved bound for Kakeya type maximal functions
• L p Estimates for the X-Ray Transform Restricted to Line Complexes of Kirillov Type
• Fourier integral operators with cusp singularities
• On X-ray transforms for rigid line complexes and integrals over curves in $\mathbb {R}^4$
• Fourier integral operators with fold singularities.
• An Estimate For a Restricted X-Ray Transform
• 𝐿^{𝑝} improving bounds for averages along curves

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