1. Given $f(x)=a \sin x+\sqrt[2019]{x}+1(a \in \mathbf{R})$, $f\left(\lg \log _{2} 10\right)=3$. Then $f(\lg \lg 2)=$
,$- 1 .-1$.
Let $g(x)=f(x)-1=a \sin x+\sqrt[2019]{x}$. Since $g(x)$ is an odd function,
$$
\begin{array}{l}
\Rightarrow f(-x)-1=-(f(x)-1) \\
\Rightarrow f(-x)=-f(x)+2 .
\end{array}
$$

Also, $\lg \lg 2=-\lg \log _{2} 10$, so $f(\lg \lg 2)=-f\left(\lg \log _{2} 10\right)+2=-1$.