Spherical convolution operators in spaces of variable Holder order

In this paper, we study the images of operators of the type of spherical potential of complex order and of spherical convolutions with kernels depending on the inner product and having a spherical harmonic multiplier with a given asymptotics at infinity. Using theorems on the action of these operators in Holder-variable spaces, we construct isomorphisms of these spaces. In Holder spaces of variable order, we study the action of spherical potentials with singularities at the poles of the sphere. Using stereographic projection, we obtain similar isomorphisms of Holder-variable spaces with respect to n-dimensional Euclidean space (in the case of its one-point compactification) with some power weights.