Extend Lemma 3.1 (Lemma 2.1) for \(\alpha otin(0,2)\). In particular, is it true that for \(-d<\alpha<0\) we have

\[
\int_{\mathbb{R}^{d}} \frac{e^{i(t, x)}}{|t|_{d}^{d+\alpha}}=(d+\alpha) C(d,-\alpha)|x|_{d}^{\alpha} \quad ?
\]