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 $\tau$.

Transport a compact system along an equivalence of types.

The set of Finset coercions forms a compact system.

A càdlàg function is locally bounded.

For $x\in[0,2\pi]$ and an interval-integrable function $g$, the norm of the localized Dirichlet-kernel integral over $[x-\pi,x+\pi]$, with cutoff $\max(1-|x-y|,0)$, is bounded by the sum of the real Carleson operators applied to $g$ and to its complex conjugate.

This is the dual of limsup_le_of_eventually_monotone_of_tendsto_on_dense.