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Transactions of the American Mathematical Society

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Singular integral operators on $ C\sp 1$ manifolds


Authors: Jeff E. Lewis, Renata Selvaggi and Irene Sisto
Journal: Trans. Amer. Math. Soc. 340 (1993), 293-308
MSC: Primary 58G15; Secondary 42B20, 47G10
DOI: https://doi.org/10.1090/S0002-9947-1993-1124170-6
MathSciNet review: 1124170
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Abstract: We show that the kernel of a singular integral operator is real analytic in $ {{\mathbf{R}}^n}\backslash \{ 0\} $ iff the symbol [Fourier transform] is real analytic in $ {{\mathbf{R}}^n}\backslash \{ 0\} $. The singular integral operators with continuous coefficients and real analytic kernels (symbols) form an operator algebra with the usual symbolic calculus. The symbol is invariantly defined under $ {C^1}$ changes of coordinates.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1993-1124170-6
Keywords: Layer potentials, nonsmooth domains, pseudodifferential operators, singular integrals, symbolic calculus
Article copyright: © Copyright 1993 American Mathematical Society

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