Improved local smoothing estimate for the wave equation in higher dimensions

DOI10.1016/j.jfa.2023.109879OpenAlexW4320719000MaRDI QIDQ2689342

Chuanwei Gao, Bochen Liu, Yakun Xi, Chang Xing Miao

Publication date: 10 March 2023

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.06870

zbMATH Keywords

wave equationlocal smoothing\(k\)-broad ``norm

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Initial value problems for second-order hyperbolic equations (35L15) Fourier integral operators applied to PDEs (35S30)

Cites Work

• Unnamed Item
• On the cone multiplier in \(\mathbb R^3\)
• Radial Fourier multipliers in high dimensions
• Kakeya sets of curves
• On the multilinear restriction and Kakeya conjectures
• \(L^p\) estimates for the waves equation
• Propagation of singularities and maximal functions in the plane
• Wave front sets, local smoothing and Bourgain's circular maximal theorem
• Negative results for Nikodym maximal functions and related oscillatory integrals in curved space
• A local smoothing estimate in higher dimensions.
• Local smoothing type estimates on \(L^p\) for large \(p\)
• Restriction estimates using polynomial partitioning. II
• A bilinear approach to cone multipliers. II: Applications
• \(L^p\)-\(L^q\) local smoothing estimates for the wave equation via \(k\)-broad Fourier restriction
• A cone restriction estimate using polynomial partitioning
• A sharp square function estimate for the cone in \(\mathbb{R}^3\)
• Sharp estimates for oscillatory integral operators via polynomial partitioning
• Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds
• The proof of the \(l^2\) decoupling conjecture
• L p regularity of averages over curves and bounds for associated maximal operators
• On plate decompositions of cone multipliers
• Sharp Local Smoothing Estimates for Fourier Integral Operators
• Improved decay of conical averages of the Fourier transform
• Square function estimates and local smoothing for Fourier integral operators
• Improved local smoothing estimates for the fractional Schrödinger operator

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