Sharp smoothing properties of averages over curves

DOI10.1017/fmp.2023.2OpenAlexW4320018258MaRDI QIDQ5877965

Hyerim Ko, Sewook Oh, Sanghyuk Lee

Publication date: 16 February 2023

Published in: Forum of Mathematics, Pi (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2105.01628

zbMATH Keywords

local smoothing\(l^p\) Sobolev regularity

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Convolution, factorization for one variable harmonic analysis (42A85)

Related Items (3)

Real analysis, harmonic analysis and applications. Abstracts from the workshop held July 3--9, 2022 ⋮ Remarks on dimension of unions of curves ⋮ \(L^2\) estimates for a Nikodym maximal function associated to space curves

Cites Work

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• Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three
• On the cone multiplier in \(\mathbb R^3\)
• Averages in the plane over convex curves and maximal operators
• Estimates for maximal functions associated with hypersurfaces in \(\mathbb R^3\) and related problems of harmonic analysis
• Regularity of solutions to the Schrödinger equation
• Propagation of singularities and maximal functions in the plane
• Wave front sets, local smoothing and Bourgain's circular maximal theorem
• Averages over curves with torsion
• Local smoothing estimates related to the circular maximal theorem
• Local smoothing type estimates on \(L^p\) for large \(p\)
• Singular and maximal Radon transforms: Analysis and geometry
• A bilinear approach to cone multipliers. II: Applications
• \(L^p\)-Sobolev estimates for a class of integral operators with folding canonical relations
• Sobolev improving for averages over curves in \(\mathbb{R}^4\)
• Maximal estimates for averages over space curves
• A sharp square function estimate for the cone in \(\mathbb{R}^3\)
• The proof of the \(l^2\) decoupling conjecture
• Restriction estimates for space curves with respect to general measures
• A Calderón–Zygmund estimate with applications to generalized Radon transforms and Fourier integral operators
• Problems on averages and lacunary maximal functions
• Endpoint bounds for a generalized Radon transform
• L p regularity of averages over curves and bounds for associated maximal operators
• Packing Circles in the Plane
• Local Smoothing Properties of Dispersive Equations
• Maximal functions: Spherical means
• Problems in harmonic analysis related to curvature
• A Kakeya-type problem for circles
• On a Problem Related to Sphere and Circle Packing
• Endpoint estimates for the circular maximal function
• 𝐿^{𝑝} improving bounds for averages along curves
• A short proof of ℓ2 decoupling for the moment curve
• A generalization of Bourgain’s circular maximal theorem

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