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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

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.

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
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