Averages of functions over hypersurfaces in \(\mathbb R^n\)
From MaRDI portal
Publication:580618
DOI10.1007/BF01388869zbMath0626.42009OpenAlexW1964539058MaRDI QIDQ580618
Elias M. Stein, Christopher D. Sogge
Publication date: 1985
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/143299
Maximal functions, Littlewood-Paley theory (42B25) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38)
Related Items (68)
Maximal functions and Fourier transforms ⋮ An almost-orthogonality principle with applications to maximal functions associated to convex bodies ⋮ Sharp maximal estimates for doubly oscillatory integrals ⋮ Applications of Multivariate Asymptotics I: Boundedness of a maximal operator on ⋮ Harmonic analysis on nilpotent groups and singular integrals. II: Singular kernels supported on submanifolds ⋮ Decay of the Fourier transform of surfaces with vanishing curvature ⋮ On the Fourier transform of measures carried by submanifolds of finite type ⋮ Convolution kernels of 2D Fourier multipliers based on real analytic functions ⋮ The weak-type (1,1) of Fourier integral operators of order –(n–1)/2 ⋮ Averages over hypersurfaces. II ⋮ Multi-parameter maximal operators associated with finite measures and arbitrary sets of parameters ⋮ Oscillatory integrals and atoms on the unit sphere ⋮ On boundedness of maximal operators associated with hypersurfaces ⋮ Maximal averages over surfaces ⋮ Oscillatory integrals and maximal averages over homogeneous surfaces ⋮ The weak type \(L^ 1\) convergence of eigenfunction expansions for pseudodifferential operators ⋮ Global range estimates for maximal oscillatory integrals with radial test functions ⋮ Damped oscillatory integrals and the boundedness problem for maximal operators ⋮ Optimal local well-posedness theory for the kinetic wave equation ⋮ Estimates for maximal functions associated with hypersurfaces in \(\mathbb R^3\) and related problems of harmonic analysis ⋮ On the boundedness of the maximal operators associated with singular hypersurfaces ⋮ The triangle averaging operator ⋮ On some properties of sparse sets: a survey ⋮ Unnamed Item ⋮ Bilinear maximal functions associated with degenerate surfaces ⋮ Weierstrass polynomials in estimates of oscillatory integrals ⋮ On estimates for maximal operators ⋮ Averages over hypersurfaces. Smoothness of generalized Radon transforms ⋮ Sharp Regularizing Estimates for the Gain Term of the Boltzmann Collision Operator ⋮ Lattice points in large convex planar domains of finite type ⋮ Smooth and singular maximal averages over 2D hypersurfaces and associated Radon transforms ⋮ Maximal averages over certain non-smooth and non-convex hypersurfaces ⋮ On estimates for oscillatory integrals with phase depending on parameters ⋮ The asymptotic property of the hyperparabolic maximal function ⋮ Strichartz estimates for orthonormal families of initial data and weighted oscillatory integral estimates ⋮ Pointwise ergodic theorems for radial averages on simple Lie groups. II ⋮ Maximal functions associated with nonisotropic dilations of hypersurfaces in \(\mathbb R^3\) ⋮ Estimates of oscillatory integrals with a damping factor ⋮ A maximal Fourier integral operator and an application ⋮ An improved remainder estimate in the Weyl formula for the planar disk ⋮ Hilbert Transforms and Maximal Functions Associated to Flat Curves on the Heisenberg Group ⋮ Maximal operators and differentiation theorems for sparse sets ⋮ Damped oscillatory integrals and boundedness of maximal operators associated to mixed homogeneous hypersurfaces ⋮ Regularity theory for the spatially homogeneous Boltzmann equation with cut-off ⋮ On averaging operators associated with convex hypersurfaces of finite type ⋮ Maximal functions over hypersurfaces with flat points. ⋮ Sobolev estimates for averaging operators over a convex hypersurface in \(\mathbb R^3\) ⋮ Estimates for the wave kernel near focal points on compact manifolds ⋮ Uniform bounds for Fourier transforms of surface measures in R$^3$ with nonsmooth density ⋮ Damped oscillatory integrals and maximal operators ⋮ On the Weierstrass Preparation Theorem ⋮ The boundedness of maximal operators associated with singular surfaces ⋮ Fourier transforms of indicator functions, lattice point discrepancy, and the stability of integrals ⋮ \(L^p\)-Sobolev estimates for a class of integral operators with folding canonical relations ⋮ Lattice points in rotated convex domains ⋮ Regularity of averages over hypersurfaces ⋮ Oscillatory Integrals and Fourier Transforms of Surface Carried Measures ⋮ Maximal averages over hypersurfaces and the Newton polyhedron ⋮ Maximal operators associated with commutators of spherical means ⋮ On Maximal Functions Associated to Hypersurfaces and the Cauchy Problem for Strictly Hyperbolic Operators ⋮ $L^{p}$ boundedness of maximal averages over hypersurfaces in $\mathbb {R}^{3}$ ⋮ Inequalities for Some Maximal Functions. II ⋮ Uniform \(L^p\) boundedness for oscillatory singular integrals with \(C^\infty\) Phases ⋮ Damping oscillatory integrals ⋮ \(L^p\)-improving bounds and weighted estimates for maximal functions associated with curvature ⋮ The dimension-free estimate for the truncated maximal operator ⋮ On the boundedness problem of maximal operators ⋮ \(L^ p\) regularity for the wave equation with strictly convex obstacles
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Estimates for the Fourier transform of the characteristic function of a convex set
- Maximal functions: Spherical means
- Problems in harmonic analysis related to curvature
- On the Asymptotic Behavior of the Fourier Transform of the Indicator Function of a Convex Set
- Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63)
This page was built for publication: Averages of functions over hypersurfaces in \(\mathbb R^n\)