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arXiv · 2601.04528

Hardy decomposition of first order Lipschitz functions by Lam\'e-Navier solutions

Daniel Alfonso Santiesteban·Ricardo Abreu Blaya·Daniel Alpay
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Abstract

The Clifford algebra language allows us to rewrite the Lam\'e-Navier system in terms of the Euclidean Dirac operator. In this paper, the main question we shall be concerned with is whether or not a higher order Lipschitz function on the boundary $\Gamma$ of a Jordan domain $\Omega\subset\mathbb{R}^m$ can be decomposed into a sum of the two boundary values of a solution of the Lam\'e-Navier system with jump across $\Gamma$. Our main tool are the Hardy projections related to a singular integral operator arising in the context of Clifford analysis, which turns out to be an involution operator on the first order Lipschitz classes.

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Daniel Alfonso Santiesteban, Ricardo Abreu Blaya, Daniel Alpay. 2026-01-08. Hardy decomposition of first order Lipschitz functions by Lam\'e-Navier solutions. https://arxiv.org/abs/2601.04528

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