Abstract
We consider linear integral operators with multidimensional partial integrals in anisotropic Lebesgue spaces Lr(D) of functions defined in a finite parallelepiped D in the Euclidean spaces ℝn, where n ≥ 3. We obtain conditions on kernels of partial integrals and connections between multiindices r and p guaranteeing the boundedness of the partial integrals acting from Lr(D) to Lp(D).
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