Quantitative scalar multiplication in Morrey seminorms #
The absolute scalar factor is retained in the bound, including when the scalar vanishes or the unscaled seminorm is infinite.
theorem
CKN.Core.Endgame.morreyNorm_const_mul_le
{P τ : ℝ}
(hP : 0 < P)
(c : ℝ)
(f : Foundation.Parabolic.ParabolicPoint → ℝ)
:
(Foundation.Parabolic.Morrey.morreyNorm P τ fun (z : Foundation.Parabolic.ParabolicPoint) => c * f z) ≤ ENNReal.ofReal |c| * Foundation.Parabolic.Morrey.morreyNorm P τ f
Multiplication by a real constant scales the Morrey seminorm by at most its absolute value. No measurability or finiteness assumptions are needed.