RK-transform with γ ∈ (0, 2] of weighted spherical means of functions and asgeirsson relations.

The article examines the Radon-Kipriyanov transform (RKγ-transform) of radial functions, one-variable functions and weighted spherical means of multivariable functions. It explores the use of fractional differentiation operator with an order generated by the weight index to derive the inversion formulas for RKγ-transform of weighted spherical means, and the influence of the dimension of the Euclidean space on such formulas. Moreover, it analyzes the significant relationship between the Abel transform and the RKγ-transform of particular functions.