On local smoothing problems and Stein’s maximal spherical means

DOI10.1090/PROC/13313zbMath1379.42008arXiv1606.00080OpenAlexW3100265457MaRDI QIDQ5351788

Jianwei Yang, Ji Qiang Zheng, Chang Xing Miao

Publication date: 30 August 2017

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

Full work available at URL: https://arxiv.org/abs/1606.00080

zbMATH Keywords

wave equationlocal smoothingoscillatory integralmaximal spherical means

Mathematics Subject Classification ID

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

Related Items (3)

\(L^p -L^q\) estimates for generalized spherical averages ⋮ Endpoint estimates and optimality for the generalized spherical maximal operator on radial functions ⋮ Maximal estimates for a generalized spherical mean Radon transform acting on radial functions

Cites Work

• Averages in the plane over convex curves and maximal operators
• Characterizations of Hankel multipliers
• Propagation of singularities and maximal functions in the plane
• Wave front sets, local smoothing and Bourgain's circular maximal theorem
• Local smoothing estimates related to the circular maximal theorem
• Maximal averages over surfaces
• A local smoothing estimate in higher dimensions.
• On some variants of the Kakeya problem
• Local smoothing type estimates on \(L^p\) for large \(p\)
• The proof of the \(l^2\) decoupling conjecture
• Classical Fourier Analysis
• Local Smoothing of Fourier Integral Operators and Carleson-Sjolin Estimates
• Maximal functions: Spherical means
• A generalization of Bourgain’s circular maximal theorem
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