The author claims to have used Holder's inequality, but as I understand Holder's inequality is used to estimate the norm of the product of two functions yet here the result shows a sum in the righthand side of the following inequality, am I missing something, or did the author forget to mention an other result he used?
Note that $Q_T:=\Omega \times (0,T)$ where $\Omega \subset \mathbb{R}^d$ is an open bounded set with regular boundary and $\epsilon>0$.
