Weighted homogeneous distribution and its applications

The aim of the article is to study the relationship between the continuation of the weighted homogeneous distribution and the weighted fundamental solution of an elliptic operator with Bessel operators acting with respect to each argument. This problem for not weighted distribution was considered by Hörmander and our results are a generalization of his results. In addition, the Dirichlet problem is considered and an equality is obtained that gives a connection between the boundary condition and the solution of this Dirichlet problem by means of the Riesz $B$-potential.