Polynomial Carleson operators along monomial curves in the plane

DOI10.1007/s12220-017-9790-7zbMath1388.42040arXiv1605.05812OpenAlexW3100417822MaRDI QIDQ1747538

Po-Lam Yung, Joris Roos, Shaoming Guo, Lillian Beatrix Pierce

Publication date: 8 May 2018

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.05812

zbMATH Keywords

Radon transformsoscillatory integralsCarleson operators

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Radon transform (44A12)

Related Items (11)

Single annulus estimates for the variation-norm Hilbert transforms along Lipschitz vector fields ⋮ Uniform bounds for oscillatory and polynomial Carleson operators ⋮ Vector valued maximal Carleson type operators on the weighted Lorentz spaces ⋮ Lp$L^p$ bound for the Hilbert transform along variable non‐flat curves ⋮ Maximal polynomial modulations of singular Radon transforms ⋮ Estimates for Hilbert transforms along variable general curves ⋮ Analysis and applications: The mathematical work of Elias Stein ⋮ The Hilbert transform along the parabola, the polynomial Carleson theorem and oscillatory singular integrals ⋮ Hilbert transforms along double variable fractional monomials ⋮ \(L^p\) boundedness of Carleson \& Hilbert transforms along plane curves with certain curvature constraints ⋮ Bounds for anisotropic Carleson operators

Cites Work

• Oscillatory integrals related to Carleson's theorem: fractional monomials
• The (weak-\(L^{2}\)) boundedness of the quadratic Carleson operator
• Maximal and singular integral operators via Fourier transform estimates
• Hilbert transforms along curves. I: Nilpotent groups
• Calderón-Zygmund theory for operator-valued kernels
• A proof of boundedness of the Carleson operator
• Oscillatory integrals related to Carleson's theorem
• The polynomial Carleson operator
• \(\ell^p(\mathbb{Z}^d)\)-estimates for discrete operators of Radon type: maximal functions and vector-valued estimates
• A polynomial Carleson operator along the paraboloid
• \(L^p\) estimates for the Hilbert transforms along a one-variable vector field
• On convergence and growth of partial sums of Fourier series
• On weighted norm inequalities for the Carleson and Walsh-Carleson operator
• Problems in harmonic analysis related to curvature
• Some new light on a few classical results
• The estimation of an integral arising in multiplier transformations
• Pointwise convergence of Fourier series

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