Abstract
A function valued in a Euclidean Clifford algebra naturally decomposes into even and odd parts. When such a function is in the kernel of the Cauchy–Riemann Dirac operator, so called monogenic, these components serve as generalizations of the conjugate harmonic components of an analytic function as well as Stein–Weiss systems. Our results are in the upper half space. We show that the even and odd parts simultaneously have non-tangential boundary values almost everywhere. Moreover, we show that the even part is in the harmonic Hardy space, for \(p > 1\), if and only if the odd part is as well. With extra assumptions, this result also holds for \(p = 1\).
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