Lp Markov-Bernstein Inequalities on Arcs of the Circle

Abstract

Abstract Let 0 p α β ⩽2 π . We prove that for trigonometric polynomials s n of degree ⩽ n , we have[formula]where c is independent of α ,  β ,  n ,  s n . The essential feature is the uniformity in α and β of the estimate. The result may be viewed as an L p form of Videnskii's inequalities.