Cauchy integrals,Calderón projectors,and Toeplitz operators on uniformly rectifiable domains |
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Authors: | Irina Mitrea Marius Mitrea Michael Taylor |
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Institution: | 1. Department of Mathematics, Temple University, Philadelphia, PA 19122, USA;2. Department of Mathematics, University of Missouri at Columbia, Columbia, MO 65211, USA;3. Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599-3250, USA |
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Abstract: | 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 Lp(∂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. |
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Keywords: | 31B10 35J46 45B05 45E05 49Q15 |
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