Markov's inequality on Koornwinder's domain in $L^p$ norms

Tomasz Beberok

Let $\Omega =\{(x,y)\in {\mathbb{R}}^2:|x|<y+1,x^2>4y\}$. We prove that the optimal exponent in Markov's inequality on $\Omega$ in $L^p$ norms is 4.