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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Singular integral operators on $C^ 1$ manifolds
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by Jeff E. Lewis, Renata Selvaggi and Irene Sisto PDF
Trans. Amer. Math. Soc. 340 (1993), 293-308 Request permission

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
  • © Copyright 1993 American Mathematical Society
  • 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