Averages over hypersurfaces. Smoothness of generalized Radon transforms

DOI10.1007/BF02796147zbMath0695.42012OpenAlexW2056051178MaRDI QIDQ909928

Christopher D. Sogge, Elias M. Stein

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1007/bf02796147

zbMATH Keywords

maximal functionsmicrolocal analysis

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25)

Related Items

A refinement of the Strichartz inequality on the saddle and applications ⋮ Optimal local well-posedness theory for the kinetic wave equation ⋮ Uniform sublevel Radon-like inequalities ⋮ Sharp Regularizing Estimates for the Gain Term of the Boltzmann Collision Operator ⋮ Propagation of singularities and maximal functions in the plane ⋮ Pointwise ergodic theorems for radial averages on simple Lie groups. II ⋮ Sobolev estimates for operators given by averages over cones ⋮ A maximal Fourier integral operator and an application ⋮ Two endpoint bounds for generalized Radon transforms in the plane ⋮ Regularity theory for the spatially homogeneous Boltzmann equation with cut-off ⋮ Spherical means on the Heisenberg group: stability of a maximal function estimate ⋮ Radon transforms and finite type conditions ⋮ Fourier integral operators on noncompact symmetric spaces of real rank one ⋮ Maximal estimates for the bilinear spherical averages and the bilinear Bochner-Riesz operators ⋮ Degenerate Fourier integral operators in the plane ⋮ Maximal operators and Fourier transforms of self-similar measures

Cites Work

• Averages of functions over hypersurfaces in \(\mathbb R^n\)
• Averages in the plane over convex curves and maximal operators
• The boundedness of the maximal Bochner-Riesz operator on \(L^ 4\)(\(R^ 2\))
• On the Littlewood-Paley and Marcinkiewicz functions in higher dimensions
• Maximal functions and Fourier transforms
• Hilbert integrals, singular integrals, and Radon transforms. I
• Regularity of solutions to the Schrödinger equation
• Averages over hypersurfaces. II
• The weak type \(L^ 1\) convergence of eigenfunction expansions for pseudodifferential operators
• On the characteristic Cauchy problem
• Fourier integral operators. I
• Oscillatory integrals and multipliers on FL\(^p\)
• \(H^p\) spaces of several variables
• Schrodinger Equations: Pointwise Convergence to the Initial Data
• On the Almost Everywhere Convergence to L p Data for Higher Order Hyperbolic Operators
• Maximal functions: Spherical means
• Problems in harmonic analysis related to curvature
• Fourier transforms of surface-carried measures and differentiability of surface averages
• Oscillatory integrals and multiplier problem for the disc
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item