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How to get $\int_{\mathbb R^d} |\partial_i\partial_j(1-\Delta)^{-\frac{\delta}{2}}p_t(\cdot-...

We consider the Gaussian heat kernel $p_t$ on $\mathbb R^d$, i.e., $$ p_t (x) := (4\pi t)^{-\frac{d}{2}} e^{-\frac{|x|^2}{4t}}, \quad t>0, x \in \mathbb R^d, $$ and define the operator $P_t$ by $$ P_t …
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