The area integral and boundary values of octonion-valued monogenic functions

Abstract

We introduce the Area Integral for octonion-valued monogenic functions in the half-space. It is used to prove the existence of the non-tangential boundary values almost everywhere and of the normal boundary values at a given boundary point for these classes of functions. It is also proved that the non-tangential limit for the scalar component of a monogenic function and those limits for all of its other seven components exist or not exist simultaneously. It turns out that non-commutativity and non-associativity of octonions in certain problems can be circumvented by making use of P. Stein method and employing subharmonic functions.