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In this paper, we investigate properties of classes of functions related tocertain elliptic operators. Firstly, we prove that a main result of Dyakonov(Acta Math. 178(1997), 143--167) on analytic functions can be extended to thismore general setting. Secondly, we study the radial growth on these functionsand the obtained results are generalizations of the corresponding results ofMakarov (Proc. London Math. Soc. 51(1985), 369--384) and Korenblum (Bull. Amer.Math. Soc. 12(1985), 99--102). Finally, we discuss the Dirichlet type energyintegrals on such classes of functions and their applications.

Lipschitz type, radial growth and Dirichlet type spaces on functions induced by certain elliptic operators