$L^p$ regularity for a class of averaging operators on the Heisenberg group

DOI10.1512/iumj.2022.71.8914zbMath1500.43005arXiv2002.01917OpenAlexW3004745411MaRDI QIDQ5075682

Geoffrey Bentsen

Publication date: 11 May 2022

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.01917

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Function spaces arising in harmonic analysis (42B35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Radon transform (44A12) Integral operators (47G10) Analysis on other specific Lie groups (43A80) Fourier integral operators applied to PDEs (35S30)

Related Items (1)

Lacunary maximal functions on homogeneous groups

Cites Work

• Unnamed Item
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• Composition of some singular Fourier integral operators and estimates for restricted X-ray transforms
• Theory of function spaces II
• Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle
• Nonlocal inversion formulas for the X-ray transform
• Degenerate Fourier integral operators in the plane
• \(L^2\) estimates for averaging operators along curves with two-sided \(k\)-fold singularities
• Oscillatory and Fourier integral operators with degenerate canonical relations
• Spherical means on the Heisenberg group: stability of a maximal function estimate
• The proof of the \(l^2\) decoupling conjecture
• Fourier integral operators. I
• \(H^p\) spaces of several variables
• A Calderón–Zygmund estimate with applications to generalized Radon transforms and Fourier integral operators
• $L^p$-improving properties of measures supported on curves on the Heisenberg group
• Optional regularity of fourier integral operators with one-sided folds
• Fourier integral operators with fold singularities.

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