Abstract.
We consider several generalizations of the concept of an intersection body and show their connections with the Fourier transform and embeddings in L p -spaces. These connections lead to generalizations of the recent solution to the Busemann—Petty problem on sections of convex bodies.
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Submitted: October 1999, Revision: December 1999.
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Koldobsky, A. A functional analytic approach to intersection bodies . GAFA, Geom. funct. anal. 10, 1507–1526 (2000). https://doi.org/10.1007/PL00001659
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DOI: https://doi.org/10.1007/PL00001659