Nonlinear Calderón–Zygmund inequalities for maps

Abstract

Being motivated by the problem of deducing $$\mathsf {L}^{p}$$ -bounds on the second fundamental form of an isometric immersion from $$\mathsf {L}^{p}$$ -bounds on its mean curvature vector field, we prove a nonlinear Calderon–Zygmund inequality for maps between complete (possibly noncompact) Riemannian manifolds.