The Green-Tao theorem for Piatetski-Shapiro primes

Let $m\ge 3$. Suppose that $$1-2^{-2^{m^2{4}^m}}<\gamma <1.$$ Then the set $$\{p\text{ prime}:p=[n^{\frac{1}{\gamma }}]\text{ for some }n\in \mathbb{N}\}$$ contains infinitely many non-trivial $m$-term arithmetic progressions.