Mark Graev 
Intermediate inversion formulas in integral geometry
(Lobachevskii Journal of Mathematics, Vol.3, pp.97-111)

We solve the following ``intermediate'' problem of integral geometry: to reconstruct integrals of a function over $p$-dimensional planes in $\Bbb R^n$ starting from its integrals over k$-planes, where $p<k$. Some generalizations are also presented.

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