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

Andreas Rosén

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arXiv · 1211.6888

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

Andreas Rosén

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Abstract

We prove square function estimates in $L_2$ for general operators of the form $B_1D_1+D_2B_2$, 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 $B_1$ and $B_2$ are not assumed to be related in any way. We show how these operators appear naturally from exterior differential systems with boundary data in $L_2$. We also prove non-tangential maximal function estimates, where our proof needs only off-diagonal decay of resolvents in $L_2$, unlike earlier proofs which relied on interpolation and $L_p$ estimates.

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Andreas Rosén. 2012-11-29. Square function and maximal function estimates for operators beyond divergence form equations. https://arxiv.org/abs/1211.6888

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