Calderon-Zygmund theory for singular integral operators associated with second-order elliptic partial differential systems on rough subdomains of Riemannian manifolds
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[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] This dissertation is a treatise on the theory of Calderon-Zygmund type singular integral operators capable of handling boundary layer potentials arising naturally in the treatment of elliptic boundary value problems on rough subdomains of Riemannian manifolds, where the nature of the underlying domain is very general, and is best described in the language of geometric measure theory. The resulting theory is a blend of harmonic analysis, differential geometry, and geometric measure theory which includes results pertaining to nontangential boundedness and pointwise traces (jump formulas), square-function and Carleson measure estimates, as well as compactness criteria on Lebesgue and Sobolev spaces.
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