SCHWEITZER 2005 Problem 9

prove that if $r_n$ is a rational function whose numerator and denominator have at most degrees $n$ , then $$||r_n||_{1/2}+\left\|\frac{1}{r_n}\right\|_2\geq\frac{1}{2^{n-1}}$$ where $||\cdot||_a$ denotes the supremum over a circle of radius $a$ around the origin.