A necessary condition for Calderon-Zygmund singular integral operators

Calderon-Zygmund singular integral operators have been extensively studied for almost half a century. This paper provides a context for and proof of the following result: If a Calderon-Zygmund convolution singular integral operator is bounded on the Hardy space H-1(R-n), then the homogeneous of degree zero kernel is in the Hardy space H1(Sn-1) on the sphere.