Manuscript XX-C@1 · XX-C.tex · section · 7a8cab37

The exact domain of the dipole estimate

Newton inversion and uniform spatial-tail estimates › The exact domain of the dipole estimate · lines 1032–1046

XX-C@1#eq:Schwartz

For a compact interval $J ⋐ I$ , define the uniform Schwartz seminorms

p_{N, m, α; J} (b) = t \in J, x \in R^{3} sup (1 + ∣ x ∣)^{N} ∣ \partial_{t}^{m} \partial_{x}^{α} b (t, x)∣ .

They use coordinate components in a fixed smooth background trivialization.

Displayed formulas in this passage

XX-C@1#eq:Schwartz · line 1036
$p_{N, m, α; J} (b) = t \in J, x \in R^{3} sup (1 + ∣ x ∣)^{N} ∣ \partial_{t}^{m} \partial_{x}^{α} b (t, x)∣ .$