Integral Lebesgue–Kipriyanov Measure and Weighted Partial Integral Operators for Functions with Axial Spherical Symmetry

We consider a weighted partial integral operator of functions with axial spherical symmetry in the weighted Lebesgue–Kipriyanov space $$L_{p}^{\gamma}(D)$$ with the integral Lebesgue–Kipriyanov measure $$\prod_{i=1}^{n}x_{i}^{\gamma_{i}}dx_{i},\gamma_{i}{>}{-}1$$ . A criterion for the boundedness of a given operator and a linear weighted partial integral operator of functions with axial spherical symmetry in $$L_{p}^{\gamma}(D)$$ is obtained.