My professor asked me to derive this inverse estimate:
$\|{v}\|_{W^{m,p}(T)} \le C|T|^{1/p - 1/q} \cdot h_{T}^{l-m} \cdot \|{v}\|_{W^{l,q}(T)}$, for $l \le m$
So I divided the problem into 2 steps: $l=0$ and $l\neq 0$ and I know how to obtain the general result for $l\neq 0$ using the case $l=0$. But to use it I need to prove this inequality first:
$\|{v}\|_{W^{m,p}(T)} \le C|T|^{1/p - 1/q} \cdot h_{T}^{-m} \cdot \|{v}\|_{L^{q}(T)}$
Could someone, please, help me with proof or with any hints? Thanks!