Pointwise bilinear tensor bound #
The mollifier L²-to-pointwise estimate controls the rank-one tensor at each spatial point before taking its L² norm.
theorem
CKN.Leray.regularisedSchwartzTensorBilinear_pointwise_norm_le
(ρ : RegMollifierProfile)
(ε : ℝ)
(hε : 0 < ε)
:
∃ (C : ℝ),
0 ≤ C ∧ ∀ (g f : SchwartzMap Foundation.Parabolic.L2Vec3 ComplexVec3) (x : Foundation.Parabolic.L2Vec3),
‖(regularisedSchwartzTensorBilinear ρ ε hε g f) x‖ ≤ C * ‖g.toLp 2 MeasureTheory.volume‖ * ‖f x‖
One mollifier constant controls the pointwise tensor norm by the first field's L² norm and the second field's pointwise norm.