Geodesic
Sharpness Results and Knapp’s Homogeneity Argument
Canadian mathematical bulletin, Tome 43 (2000) no. 1, pp. 63-68

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DOI

We prove that the ${{L}^{2}}$ restriction theorem, and ${{L}^{p}}\,\to \,{{L}^{{{p}'}}}\,,\,\frac{1}{p}\,+\,\frac{1}{{{p}'}}\,=\,1$ , boundedness of the surface averages imply certain geometric restrictions on the underlying hypersurface. We deduce that these bounds imply that a certain number of principal curvatures do not vanish.
DOI : 10.4153/CMB-2000-009-7
Mots-clés : 42B99 
Iosevich, Alex; Lu, Guozhen. Sharpness Results and Knapp’s Homogeneity Argument. Canadian mathematical bulletin, Tome 43 (2000) no. 1, pp. 63-68. doi: 10.4153/CMB-2000-009-7
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     title = {Sharpness {Results} and {Knapp{\textquoteright}s} {Homogeneity} {Argument}},
     journal = {Canadian mathematical bulletin},
     pages = {63--68},
     year = {2000},
     volume = {43},
     number = {1},
     doi = {10.4153/CMB-2000-009-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2000-009-7/}
}
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