Weighted Riesz potentials: Singular problems (Q1594234)

\textit{M. Riesz} [Acta Math. 81, 1-223 (1949; Zbl 0033.27601)] developed a method of solution for the Cauchy problem in the case of hyperbolic partial differential equations and a general method for the regularization of divergent integrals as applied to solving differential equations by analytic continuation. The author extends Riesz's approach to multidimensional weight Riemann-Liouville integrals, and applies it to singular partial differential equations. He calls the corresponding potentials `weight Riesz potentials'.