Blowup Riesz Linear #
Pressure reconstruction and convergence bounds for the rescaled sequence.
theorem
ESS.blowup_rieszPressureSpaceTime_add_ae
(F G : Fin 3 → Fin 3 → CKN.Foundation.Parabolic.Vec3 × ℝ → ℝ)
(hF : ∀ (i j : Fin 3), MeasureTheory.MemLp (F i j) (ENNReal.ofReal (3 / 2)) MeasureTheory.volume)
(hG : ∀ (i j : Fin 3), MeasureTheory.MemLp (G i j) (ENNReal.ofReal (3 / 2)) MeasureTheory.volume)
:
let H := fun (i j : Fin 3) (z : CKN.Foundation.Parabolic.Vec3 × ℝ) => F i j z + G i j z;
have hH := ⋯;
CKN.Leray.rieszPressureSpaceTime (3 / 2) blowup_rieszPressureSpaceTime_add_ae._proof_1 H hH =ᵐ[MeasureTheory.volume]
fun (z : CKN.Foundation.Parabolic.Vec3 × ℝ) =>
CKN.Leray.rieszPressureSpaceTime (3 / 2) blowup_rieszPressureSpaceTime_add_ae._proof_1 F hF z + CKN.Leray.rieszPressureSpaceTime (3 / 2) blowup_rieszPressureSpaceTime_add_ae._proof_1 G hG z
The canonical space-time Riesz pressure is additive as an almost-everywhere defined function of its tensor input.