Spherical means and the restriction phenomenon
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Publication:5943954
DOI10.1007/BF02514502zbMath0989.42002MaRDI QIDQ5943954
Luca Brandolini, Giancarlo Travaglini, Alexander Iosevich
Publication date: 9 July 2002
Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/59688
rotationspherical meansconvex curvefractal measureGaussian curvaturerestriction of the Fourier transform
Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Measures on groups and semigroups, etc. (43A05) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25)
Related Items (5)
Convex curves, Radon transforms and convolution operators defined by singular measures ⋮ L p Mixed-norm estimates for convolution operator defined by singular measures ⋮ Lattice points and generalized Diophantine conditions ⋮ Restriction for homogeneous polynomial surfaces in $\mathbb {R}^3$ ⋮ Restriction for flat surfaces of revolution in ${\mathbf R}^3$
Cites Work
- Estimates for translation invariant operators in \(L^p\) spaces
- Irregularities of distribution. I
- Convex hypersurfaces and Fourier transforms
- Average decay of Fourier transforms and integer points in polyhedra
- Average decay of Fourier transforms and geometry of convex sets
- Hausdorff dimension and distance sets
- Maximal averages over surfaces
- Pointwise convergence of Fejér type means
- How large are the spectral gaps?
- Some remarks on restriction of the Fourier transform for general measures
- A note on spherical summation multipliers
- Convex curves, Radon transforms and convolution operators defined by singular measures
- Sharp estimates for the Bochner-Riesz operator of negative order in $\mathbf {R}^2$
- On the Asymptotic Behavior of the Fourier Transform of the Indicator Function of a Convex Set
- Lattice points and generalized Diophantine conditions
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