The Phragemén‐Lindelöf principle of harmonic functions and conditions for nevanlinna class in the half space

In this article, we firstly discuss a kind of Phragemén‐Lindelöf Principle of harmonic functions by using the Nevanlinna's representation in the high dimensional space. Secondly, we derive the sufficient conditions for subharmonic functions being in the Nevanlinna class as well. These results are main tools to study the Hilbert space of harmonic functions with analytic approaches and generalizations of some classic results.