Singular integral operators on 𝐶¹ manifolds

Lewis, Jeff E.; Selvaggi, Renata; Sisto, Irene

doi:10.1090/S0002-9947-1993-1124170-6

Singular integral operators on $C^ 1$ manifolds
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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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