Square function and maximal function estimates for operators beyond divergence form equations

2012/11/29 by Rosén, Andreas
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1211.6888

Abstract

We prove square function estimates in L₂ for general operators of the form B₁D₁+D₂B₂, where D_i are partially elliptic constant coefficient homogeneous first order self-adjoint differential operators with orthogonal ranges, and B_i are bounded accretive multiplication operators, extending earlier estimates from the Kato square root problem to a wider class of operators. The main novelty is that B₁ and B₂ are not assumed to be related in any way. We show how these operators appear naturally from exterior differential systems with boundary data in L₂. We also prove non-tangential maximal function estimates, where our proof needs only off-diagonal decay of resolvents in L₂, unlike earlier proofs which relied on interpolation and L_p estimates.

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