  We prove extensions of classical concentration inequalities for random
variables which have $\alpha$-subexponential tail decay for any $\alpha \in
(0,2]$. This includes Hanson--Wright type and convex concentration
inequalities. We also provide some applications of these results. This includes
uniform Hanson--Wright inequalities and concentration results for simple random
tensors in the spirit of previous work by Klochkov--Zhivotovskiy and Vershynin.
