The Lebesgue constant for uniform approximation of differential forms

In this work we address the problem of uniform approximation of differential forms starting from weak data defined by integration on rectifiable sets. We study approximation schemes defined by the projection operator L given by either generalized weighted least squares or interpolation. We show that, under a natural measure theoretic condition, the norm of such operator equals the Lebesgue constant of the problem. We finally estimate how the Lebesgue constant varies under the action of smooth mappings from the reference domain to a physical one, as is customarily done e.g. in finite element method.