Orders of strong and weak averaging principle for multiscale SPDEs driven by $alpha$-stable process

In this paper, the averaging principle is studied for a class of multiscale stochastic partial differential equations driven by $alpha$-stable process, where $alphain(1,2)$. Using the technique of Poisson equation, the orders of strong and weak convergence are given $1-1/alpha$ and $1-r$ for any $rin (0,1)$ respectively. The main results extend Wiener noise considered by Br{e}hier in [6] and Ge et al. in [17] to $alpha$-stable process, and the finite dimensional case considered by Sun et al. in [39] to the infinite dimensional case.