Abstract
In this paper, we investigate some properties of solutions f to the nonhomogenous Yukawa equation Δf(z) = λ(z)f(z) in the unit ball \(\mathbb{B}^n\) of ℂn, where λ is a real function from \(\mathbb{B}^n\) into ℝ. First, we prove that a main result of Girela, Pavlović and Peláez (J. Analyse Math. 100 (2006), 53–81) on analytic functions can be extended to this more general setting. Then we study relationships on such solutions between the bounded mean oscillation and Lipschitz-type spaces. The obtained result generalized the corresponding result of Dyakonov (Acta Math. 178 (1997), 143–167). Finally, we discuss Dirichlet-type energy integrals on such solutions in the unit ball of ℂn and give an application.
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Chen, S., Rasila, A. & Wang, X. Radial growth, Lipschitz and Dirichlet spaces on solutions to the non-homogenous Yukawa equation. Isr. J. Math. 204, 261–282 (2014). https://doi.org/10.1007/s11856-014-1092-1
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DOI: https://doi.org/10.1007/s11856-014-1092-1