A method for proving \(L^p\)-boundedness of singular Radon transforms in codimension 1

DOI10.1215/S0012-7094-01-10826-0zbMath1015.42008OpenAlexW2070715919MaRDI QIDQ1847843

Michael Greenblatt

Publication date: 27 October 2002

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-01-10826-0

zbMATH Keywords

\(L^p\)-boundednesssingular integralRadon transformCalderón-Zygmund operators\(L^p\)-estimate

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Function spaces arising in harmonic analysis (42B35) Radon transform (44A12)

Related Items (8)

Real analytic multi-parameter singular Radon transforms: Necessity of the Stein-Street condition ⋮ Singular Radon transforms and maximal functions under convexity assumptions ⋮ 𝐿^{𝑝} improving bounds for averages along curves ⋮ A \(T(1)\) theorem for singular Radon transforms ⋮ Variational methods for tomographic reconstruction with few views ⋮ A variational method using fractional order Hilbert spaces for tomographic reconstruction of blurred and noised binary images ⋮ Singular integral operators with kernels associated to negative powers of real-analytic functions ⋮ $L^p$ regularity of averaging operators with higher fold singularities

Cites Work

• Maximal and singular integral operators via Fourier transform estimates
• Balls and metrics defined by vector fields. I: Basic properties
• Hilbert transforms along curves. I: Nilpotent groups
• Harmonic analysis on nilpotent groups and singular integrals. I: Oscillatory integrals
• Hilbert integrals, singular integrals, and Radon transforms. I
• Uniform estimates for oscillatory integral operators
• Singular integrals associated to hypersurfaces: \(L^2\) theory
• Degenerate Fourier integral operators in the plane
• The Newton polyhedron and oscillatory integral operators
• Sobolev estimates for fractional and singular Radon transforms
• Singular and maximal Radon transforms: Analysis and geometry
• Estimates for singular Radon transforms and pseudodifferential operators with singular symbols
• Singular integrals related to the Radon transform and boundary value problems
• Maximal functions associated to smooth curves
• Radon transforms and finite type conditions
• Classes of singular integrals along curves and surfaces
• On X-ray transforms for rigid line complexes and integrals over curves in $\mathbb {R}^4$
• Singular integrals and partial differential equations of parabolic type
• Unnamed Item
• Unnamed Item

This page was built for publication: A method for proving \(L^p\)-boundedness of singular Radon transforms in codimension 1