Sharp \(L^p-L^q\) estimates for a class of averaging operators

DOI10.5802/AIF.1553zbMath0898.42003OpenAlexW2312997452MaRDI QIDQ671234

Eric T. Sawyer, Alexander Iosevich

Publication date: 27 February 1997

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1996__46_5_1359_0

zbMATH Keywords

norm inequalityhypersurfacesaveraging operatorshomogeneous functions

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10)

Related Items (10)

Averaging operators over homogeneous varieties over finite fields ⋮ Weighted norm inequalities for $k$-plane transforms ⋮ Maximal averages over surfaces ⋮ Three new results on continuation criteria for the 3D relativistic Vlasov-Maxwell system ⋮ Uniform sublevel Radon-like inequalities ⋮ Smoothing theorems for Radon transforms over hypersurfaces and related operators ⋮ Extension and averaging operators for finite fields ⋮ Hyperplane integrability conditions and smoothing for Radon transforms ⋮ Generalized curvature for certain Radon-like operators of intermediate dimension ⋮ \(L^p\)-improving bounds and weighted estimates for maximal functions associated with curvature

Cites Work

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• Maximal operators associated to families of flat curves in the plane
• Harmonic analysis on nilpotent groups and singular integrals. III: Fractional integration along manifolds
• Oscillatory integrals and maximal averages over homogeneous surfaces
• Averages over homogeneous hypersurfaces in
• Convolutions with Kernels Having Singularities on a Sphere
• 𝐿^{𝑝} boundedness of certain convolution operators

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