The connection between the Cegrell classes and compliant functions

Rafal Czyz}, Per Åhag

Abstract


In this article the connection between the Cegrell classes and compliant functions is studied. A suitable norm is constructed which makes the compliant functions into a Banach space. As an application a characterization of the Dirichlet problem for pluriharmonic functions is achieved. Explicit examples of non-compliant functions will be constructed and a sufficient condition for compliance will be proved.

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DOI: http://dx.doi.org/10.7146/math.scand.a-15001

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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