Partial Integrals in Anisotropic Lebesgue Spaces. II: Multidimensional Case

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).