Blowup Riesz Slice Bound

Pressure reconstruction and convergence bounds for the rescaled sequence.

theorem ESS.blowup_rieszPressureSpaceTime_slice_norm_bound (F : 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) {a b : ℝ} (M : ℝ) (hinput : ∀ᵐ (t : ℝ) ∂MeasureTheory.volume.restrict (Set.Ioo a b), ∀ (i j : Fin 3), MeasureTheory.lpNorm (fun (x : CKN.Foundation.Parabolic.Vec3) => F i j (x, t)) (ENNReal.ofReal (3 / 2)) MeasureTheory.volume ≤ M) : ∀ᵐ (t : ℝ) ∂MeasureTheory.volume.restrict (Set.Ioo a b), MeasureTheory.MemLp (fun (x : CKN.Foundation.Parabolic.Vec3) => CKN.Leray.rieszPressureSpaceTime (3 / 2) blowup_rieszPressureSpaceTime_slice_norm_bound._proof_1 F hF (x, t)) (ENNReal.ofReal (3 / 2)) MeasureTheory.volume ∧ MeasureTheory.eLpNorm (fun (x : CKN.Foundation.Parabolic.Vec3) => CKN.Leray.rieszPressureSpaceTime (3 / 2) blowup_rieszPressureSpaceTime_slice_norm_bound._proof_1 F hF (x, t)) (ENNReal.ofReal (3 / 2)) MeasureTheory.volume ≤ ENNReal.ofReal (CKN.Leray.rieszPressureOperatorBound (3 / 2) blowup_rieszPressureSpaceTime_slice_norm_bound._proof_1 * (9 * M))

A uniform bound on the nine tensor-component slice norms gives the corresponding Riesz pressure slice bound.