Square function and maximal function estimates for operators beyond divergence form equations
Square function and maximal function estimates for operators beyond divergence form equations
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超出散度形式方程的算子的平方函数和最大函数估计
DOI：
10.1007/s00028-013-0195-1
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发表时间：
2012
影响因子：
1.4
通讯作者：
Andreas Rosén
中科院分区：
文献类型：
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作者：
Andreas Rosén
我们证明平方函数估计在L2的一般运营商的形式B1D1 + D2B2，其中Di是部分椭圆常系数齐次一阶自伴微分算子的正交范围，和Bi是有界增生乘法算子，早期的估计从加藤平方根问题扩展到更广泛的一类运营商。主要的新奇在于B1和B2不被假设以任何方式相关。我们展示了这些运营商如何自然地出现在L2的边界数据从外部微分系统。我们还证明了非切极大函数的估计，我们的证明只需要非对角衰减的预解在L2，不像以前的证明依赖于插值和Lp估计。
We prove square function estimates in L2 for general operators of the form B1D1 + D2B2, where Di are partially elliptic constant coefficient homogeneous first-order self-adjoint differential operators with orthogonal ranges, and Bi 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 Lp estimates.