Geometric BVPs, Hardy spaces, and the Cauchy integral and transform on regions with corners |
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Authors: | Paul Loya |
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Affiliation: | Department of Mathematics, Binghamton University, Vestal Parkway East, Binghamton, NY 13902, USA |
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Abstract: | In this paper we give a new perspective on the Cauchy integral and transform and Hardy spaces for Dirac-type operators on manifolds with corners of codimension two. Instead of considering Banach or Hilbert spaces, we use polyhomogeneous functions on a geometrically “blown-up” version of the manifold called the total boundary blow-up introduced by Mazzeo and Melrose [R.R. Mazzeo, R.B. Melrose, Analytic surgery and the eta invariant, Geom. Funct. Anal. 5 (1) (1995) 14-75]. These polyhomogeneous functions are smooth everywhere on the original manifold except at the corners where they have a “Taylor series” (with possible log terms) in polar coordinates. The main application of our analysis is a complete Fredholm theory for boundary value problems of Dirac operators on manifolds with corners of codimension two. |
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Keywords: | 58J28 58J52 |
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