The support of the parametrix of laplacian

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The Analysis of Linear Partial Differential Operator Vol.I 2nd Edition Page207 The proof of Lemma 7.6.3 says:

By Theorem 7.1.22 the operator$(-\Delta)^s$ has a parametrix $E$ with support in the open unit ball.

But Theorem 7.1.22 is

Every elliptic operator $P(D)$ with constant coefficients has a parametrix $E$ which is a $C^\infty$ function in $\mathbb{R}^n\setminus \left\{ 0\right\}.$

How to use it to get the support of $E$ is in the open unit ball? Or it's just an error?