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A mixed norm estimate for the X-ray transform

1998
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Revista matemática iberoamericana
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Let G be the space of lines in R 3 , i.e. the 4-dimensional manifold whose elements are all lines in R 3 . We can coordinatize G in the following way'='( e x) where e 2 S 2 nf 1g is the direction of'and x = x'is the unique point on'which is perpendicular to e. We will denote the direction e of'bỳ . The distance on G can bede ned using the standard distances on the sphere and in R 3 and this identi cation, thus d(' m) = jx'; x m j + (' m) where (' m) = (' m ) is the unoriented angle (2 0 = 2])

doi:10.4171/rmi/245
fatcat:ydigzehqcvfedba2zvp6b2ipjm