Real Analytic Multi-parameter Singular Radon Transforms: necessity of the Stein-Street condition

Lingxiao Zhang

We study operators of the form $$Tf(x)=\psi (x)\int f({\gamma }_t(x))K(t)dt,$$ where ${\gamma }_t(x)$ is a real analytic function of $(t,x)$ mapping from a neighborhood of $(0,0)$ in $\mathbb{R}…