Radial growth, Lipschitz and Dirichlet spaces on solutions to the Yukawa equation

Abstract

In this paper, we investigate some properties to solutions $f$ to the Yukawa PDE: $\Delta f=\lambda f$ in the unit ball ${\mathbb{B}}^n$ of ${\mathbb{C}}^n$, where $\lambda$ is a nonnegative constant. First, we prove that the answer to an open problem of Girela and Peláez, concerning such solutions, is positive. Then we study relationships on such solutions between the bounded mean oscillation and Lipschitz-type spaces. At last, we discuss Dirichlet-type energy integrals on such solutions in the unit ball of ${\mathbb{C}}^n$ and give an application.

18 pages