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In this paper we solve the problem on finding a sectionally Cliffordalgebra-valued harmonic function, zero at infinity and satisfying certainboundary value condition related to higher order Lipschitz functions. Our maintool are the Hardy projections related to a singular integral operator arisingin bimonogenic function theory, which turns out to be an involution operator onthe first order Lipschitz classes. Our result generalizes the classical Hardydecomposition of Holder continuous functions on a simple closed curve in thecomplex plane.

Decomposition of first order Lipschitz functions by Clifford algebra-valued harmonic functions