Calderón–Zygmund operator

Summary

A Calderón–Zygmund operator is a bounded linear operator on $L^2(\R^n)$ that is given away from the diagonal by integration against a Calderón–Zygmund kernel. This class contains the Hilbert transform, the Riesz transforms, the operators with smooth multipliers of Hörmander–Mikhlin type, and many operators that are not translation invariant. Every Calderón–Zygmund operator is bounded on $L^p(\R^n)$ for $1 < p < \infty$ and of weak type $(1, 1)$. This makes it the standard class of singular integral operators.