Geodesic
An Endpoint Estimate for Certain k-Plane Transforms
Canadian mathematical bulletin, Tome 29 (1986) no. 1, pp. 96-101

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we extend a result of Oberlin and Stein onRadon Transforms to /c-plane transforms for Specifically let where the supremum is taken over all affine k-planes ∏ parallel to the vector k-plane π. We show that F is in Ln of the Grassmann manifold Gn,k whenever f is in the Lorentz space L(n/k, 1) of Rn . The proof relies very heavily on the ideas of M. Christ.
DOI : 10.4153/CMB-1986-018-3
Mots-clés : 44A15 
Drury, S. W. An Endpoint Estimate for Certain k-Plane Transforms. Canadian mathematical bulletin, Tome 29 (1986) no. 1, pp. 96-101. doi: 10.4153/CMB-1986-018-3
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[1] 1. Christ, M., Estimates for the k-plane transform, Indiana J. Math. 33/6 (1984) pp. 891–910. Google Scholar

[2] 2. Drury, S. W., Lp estimates for the X-ray Transform, Illinois J. Math. 27/1 (1983) pp. 125–129. Google Scholar

[3] 3. Drury, S. W., Generalizations of Riesz Potentials and Lp estimates for certain k-plane transforms, Illinois J. Math. 28/3 (1984) pp. 495–512. Google Scholar

[4] 4. Falconer, K. J., Continuity properties of k-plane integrals and Besicovitch sets, Math. Proc. Cam. Phil. Soc. 87(1980), pp. 221–226. Google Scholar

[5] 5. Falconer, K. J., Sections of sets of zero Lebesgue measure, Mathematika 27 (1980), pp. 90–96. Google Scholar

[6] 6. Oberlin, D. M. and Stein, E. M., Mapping properties of the Radon transform, Indiana J. Math., 31 (1982), pp. 641–650. Google Scholar

[7] 7. Strichartz, R., Lp estimates for Radon transforms in Euclidean and non-Euclidean spaces, Duke J. Math. 48 (1981), pp. 699–727. Google Scholar

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