Cauchy integrals, Calderón projectors, and Toeplitz operators on uniformly rectifiable domains
Cauchy integrals, Calderón projectors, and Toeplitz operators on uniformly rectifiable domains
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均匀可校正域上的柯西积分、Calderón 投影仪和 Toeplitz 算子
DOI：
10.1016/j.aim.2014.09.020
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发表时间：
2015
影响因子：
1.7
通讯作者：
Michael Taylor
中科院分区：
文献类型：
--
作者：
I. Mitrea;M. Mitrea;Michael Taylor
研究了黎曼流形M中有界一致可求长域Ω上一类一阶椭圆型微分算子组D的Cauchy积分的性质。我们表明，与这样的柯西积分是类似的哈代空间的功能在Ω上湮灭的D，我们产生的投影，卡尔德龙型，到子空间的Lp（Ω）组成的边界值的元素，这样的哈代空间。我们认为Toeplitz算子与这样的预测和研究他们的指数性质。特别感兴趣的是一个“协边论参数”，这往往使人们能够确定一个粗糙UR域上的Toeplitz算子的索引与一个光滑有界域上的索引。
We develop properties of Cauchy integrals associated to a general class of first-order elliptic systems of differential operators D on a bounded, uniformly rectifiable (UR) domain Ω in a Riemannian manifold M. We show that associated to such Cauchy integrals are analogues of Hardy spaces of functions on Ω annihilated by D, and we produce projections, of Calderón type, onto subspaces of L p (∂ Ω) consisting of boundary values of elements of such Hardy spaces. We consider Toeplitz operators associated to such projections and study their index properties. Of particular interest is a “cobordism argument,” which often enables one to identify the index of a Toeplitz operator on a rough UR domain with that of one on a smoothly bounded domain.