Double Hilbert transforms along polynomial surfaces in \(\mathbb{R}^3\)

DOI10.1215/S0012-7094-00-10135-4zbMath0959.42006OpenAlexW2077068211WikidataQ125993238 ScholiaQ125993238MaRDI QIDQ1975996

Anthony Carbery, Stephen Wainger, James Wright

Publication date: 27 July 2000

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-00-10135-4

zbMATH Keywords

Newton diagramdouble Hilbert transformpolynomial surface

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Linear operators on function spaces (general) (47B38)

Related Items (10)

Real analytic multi-parameter singular Radon transforms: Necessity of the Stein-Street condition ⋮ A class of multiparameter oscillatory singular integral operators: endpoint Hardy space bounds ⋮ Multiple Hilbert transforms associated with polynomials ⋮ On singular integrals and maximal operators along surfaces of revolution on product domains ⋮ DOUBLE HILBERT TRANSFORMS ALONG POLYNOMIAL SURFACES IN R³ ⋮ Multiparameter singular integrals on the Heisenberg group: uniform estimates ⋮ Adapting product kernels to curves in the plane ⋮ A family of singular oscillatory integral operators and failure of weak amenability ⋮ Multiparameter singular integrals and maximal operators along flat surfaces ⋮ Triple Hilbert transforms along polynomial surfaces in \(\mathbb{R}^4\)

Cites Work

• Unnamed Item
• Harmonic analysis on nilpotent groups and singular integrals. I: Oscillatory integrals
• Harmonic analysis on nilpotent groups and singular integrals. II: Singular kernels supported on submanifolds
• \(L^ p\)-boundedness of the multiple Hilbert transform along a surface
• Multiparameter singular integrals and maximal functions
• The Newton polyhedron and oscillatory integral operators
• L 2 Boundedness of Hilbert Transforms Along Surfaces and Convolution Operators Homogeneous with Respect to a Multiple Parameter Group

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