Lemma (Locally constant property). Assuming that:

$f \in S (ℝ^{n})$
$supp \hat{f} \subseteq B_{1} (0)$

Then for any unit ball

B^{1} \subseteq ℝ^{n}

and any

x \in B^{'}

,

∫
∥f∥ ∞ ′ ≲ |f|(x− y)----1----dy.
L (B ) m ℝn (1+ |y|2)m