Dzhrbashyan, A. È.; Karapetyan, A. O. Integral inequalities between conjugate pluriharmonic On solution of the integral equations for the potential problems in multi-dimensional domains. (Russian. English summary) Zbl 0662.31003 Izv. Akad. Nauk Arm. SSR, Mat. 23, No. 3, 216-236 (1988). Summary: We prove inequalities between weighted \(L^p\) norms \((0<p<\infty)\) of conjugate pluriharmonic functions in different multidimensional complex domains. To do this we first prove corresponding inequalities between conjugate harmonic functions in the upper half-plane on the basis of their integral representation formula. Further for a wide class of domains in \(\mathbb C^n\) the problem is reduced to the one-dimensional case for which the solution is known. Cited in 1 Review MSC: 31A05 Harmonic, subharmonic, superharmonic functions in two dimensions 31C10 Pluriharmonic and plurisubharmonic functions 31A10 Integral representations, integral operators, integral equations methods in two dimensions Keywords:inequalities; weighted \(L^p\) norms; pluriharmonic functions; complex domains; conjugate harmonic functions; upper half-plane; integral representation PDFBibTeX XMLCite \textit{A. È. Dzhrbashyan} and \textit{A. O. Karapetyan}, Izv. Akad. Nauk Arm. SSR, Mat. 23, No. 3, 216--236 (1988; Zbl 0662.31003)