Endpoint $L^1$ estimates for Hodge systems

Abstract

In this paper we give a simple proof of the endpoint Besov-Lorentz estimate $$\Vert I_{\alpha }F{\Vert }_{{\dot{B}}_{d/(d-\alpha ),1}^{0,1}({\mathbb{R}}^d;{\mathbb{R}}^k)}\le C\Vert F{\Vert }_{L^1({\mathbb{R}}^d;{\mathbb{R}}^k)}$$ 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.

arXiv comment16 pages

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Cited by in corpus (2)

• A trace inequality for solenoidal charges
• Boundary ellipticity and limiting $L^1$-estimates on halfspaces