Asymptotic sharpness of a Bernstein-type inequality for rational functions in $H^{2}$

R. Zarouf
2012 St. Petersburg Mathematical Journal  
A Bernstein-type inequality in the standard Hardy space H 2 of the unit disc D = {z ∈ C : |z| < 1}, for rational functions in D having at most n poles all outside of 1 r D, 0 < r < 1, is considered. The asymptotic sharpness is shown as n → ∞, for every r ∈ [0, 1).
doi:10.1090/s1061-0022-2012-01198-2 fatcat:xxhawhy3trferddibrdxvnyjku