Manuscript Em02-D@4 · Em02-D-v4.tex · section · fcf2fac7

Conventions

Fixed model, root, and localization › Conventions · lines 219–245

Let

M = R^{1 + 3}, W = M^{4}_{(a, b, z, y)}, η = diag (1, - 1, - 1, - 1), □_{η} = \partial_{0}^{2} - Δ_{x} .

Pairings are complex bilinear and use coordinate volume. Component indices range over ${1, 2}$ .

For $supp Φ \subset H$ , where $H \subset W$ is compact, write

∥Φ ∥_{j, H} = J, ∣ γ ∣ \leq j max W sup ∣ \partial^{γ} Φ_{J} ∣.

For a scalar weight,

∥ w ∥_{j} = ∣ γ ∣ \leq j max M sup ∣ \partial^{γ} w ∣.

When weights depend on spectators, their seminorms include the indicated mixed derivatives. Constants may depend on the fixed compact supports and charts, but not on the test or on small $δ$ .

Displayed formulas in this passage

unlabeled · line 222
$M = R^{1 + 3}, W = M^{4}_{(a, b, z, y)}, η = diag (1, - 1, - 1, - 1), □_{η} = \partial_{0}^{2} - Δ_{x} .$
unlabeled · line 232
$∥Φ ∥_{j, H} = J, ∣ γ ∣ \leq j max W sup ∣ \partial^{γ} Φ_{J} ∣.$
unlabeled · line 238
$∥ w ∥_{j} = ∣ γ ∣ \leq j max M sup ∣ \partial^{γ} w ∣.$