Research proof index

Suppose the compatible phase system satisfies the following oscillatory cancellation estimate on every ball $B(x,r)$: for every Lipschitz amplitude $\varphi$ supported in the ball and every pair of phases $f,g$,

$\left\lVert\int_{B(x,r)}e^{i(f-g)}\varphi\right\rVert\le A\,\mu(B(x,r))\,\lVert\varphi\rVert_{\mathrm{Lip}}\,(1+d_{x,r}(f,g))^{-\tau}.$

Then the metric phase space satisfies the project’s IsCancellative property with exponent $\tau$.