Spherical Transformation of Generalized Poisson Shift and Properties of Weighted Lebesgue Classes of Functions

Abstract

We obtain a formula for the spherical transformation of generalized shift of a function depending on multiple-axial spherical symmetry. This formula shows that the generalized shift order depends on the dimension of the spherically symmetric part of the Euclidean space. The formula can be used for reducing some problems in weighted function spaces to the case of function spaces without weight. For an example we prove the global continuity with respect to shift and show that functions of class \( {C_{ev}^{\infty}}_{,0} \) are dense in the weighted Lebesgue classes.