λEnter Calculus CompanionRegistered manuscripts, kept distinct

Manuscript Em03-D@1 · Em03-D-v1.tex · section · 450d878a

An explicit local infrared and covariance estimate

An explicit local infrared and covariance estimate · lines 572–588

Em03-D@1#eq:compactcovariancebound

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For a reduced test supported at $∣ x ∣ \leq X$ , define

B_{X} (f)^{2} := \frac{C _{X} ^{2}}{2 π} [(\frac{1}{2} + \frac{2}{β ω _{c}}) ∥ f ∥_{1}^{2} + (\frac{1}{2 ω _{c} ^{2}} + \frac{2}{3 β ω _{c} ^{3}}) ∥ \partial_{t} f ∥_{1}^{2}] .

The $L^{1}$ norms are over $R^{2}$ .

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Em03-D@1#eq:compactcovariancebound · line 575
$B_{X} (f)^{2} := \frac{C _{X} ^{2}}{2 π} [(\frac{1}{2} + \frac{2}{β ω _{c}}) ∥ f ∥_{1}^{2} + (\frac{1}{2 ω _{c} ^{2}} + \frac{2}{3 β ω _{c} ^{3}}) ∥ \partial_{t} f ∥_{1}^{2}] .$

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