Endpoint $L^1$ estimates for Hodge systems

In this paper we give a simple proof of the endpoint Besov-Lorentz estimate $\|I_αF\|_{\dot{B}^{0,1}_{d/(d-α),1}(\mathbb{R}^d;\mathbb{R}^k)} \leq C \|F \|_{L^1(\mathbb{R}^d;\mathbb{R}^k)}$ for all $F \in L^1(\mathbb{R}^d;\mathbb{R}^k)$ which satisfy a first order cocancelling differential constraint. We show how this implies endpoint Besov-Lorentz estimates for Hodge systems with $L^1$ data via fractional integration for exterior derivatives.

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