On a Theorem of S.L. Sobolev Generated by Anisotropic Norms of Partial Integral Operators

A partial integral operator of the potential type acting in the anisotropic Lebesgue space of functions defined in the $$n$$ -dimensional Euclidean space is investigated. The validity of a variant of S.L. Sobolev’s first theorem on potential-type integrals for partial integral operators with infinite integration domains has been established.