Manuscript XX-D@1 · XX-D.tex · assumption · c83a526d

Assumption: Internal rod infrared bound

Native infrared conditions and the cutoff-free theorem › Internal contraction at spatial infinity · lines 1328–1346

XX-D@1#ass:internal, XX-D@1#eq:internalIR

For every compact output region $K ⋐ M$ there is $ϵ > 0$ such that, outside a fixed ball, the differentiated entries needed in (eq:drod) satisfy

∣ \partial_{t, x}^{β} d^{ia} (t, y, x)∣ \leq C_{K, β} (1 + ∣ y ∣)^{- 1 - ϵ}, (t, x) \in K .

The constants are uniform for the derivative orders required for the announced output regularity.

Displayed formulas in this passage

XX-D@1#eq:internalIR · line 1334
$∣ \partial_{t, x}^{β} d^{ia} (t, y, x)∣ \leq C_{K, β} (1 + ∣ y ∣)^{- 1 - ϵ}, (t, x) \in K .$