caa a22 4500 397533276 CHVBK 20180308164657.0 cr unu---uuuuu 161202e199506 xx s 000 0 eng 10.1112/jlms/51.3.573 doi (NATIONALLICENCE)oxford-10.1112/jlms/51.3.573 Markov and Bernstein type Inequalities in Lp for Classes of Polynomials with Constraints [Elektronische Daten] [Peter Borwein, Tamás Erdélyi] The Markov-type inequality ∫−11|f′(x)|pdx≤c(p)(n(k+1))p∫−11|f(x)|pdx is proved for all real algebraic polynomials f of degree at most n having at most k, with 0 ≤ k ≤ n, zeros (counting multiplicities) in the open unit disk of the complex plane, and for all p > 0, where c(p) = cp + 1(l + p−2) with some absolute constant c > 0. This inequality has been conjectured since 1983 when the L∞ case of the above result was proved. It improves and generalizes many earlier results. Up to the multiplicative constant c(p)> 0 the above inequality is sharp. A sharp Bernstein-type analogue for real trigonometric polynomials is also established, which is interesting on its own, and plays a key role in the proof of the Markov-type inequality. © The London Mathematical Society Notes and Papers nationallicence Borwein Peter Department of Mathematics, Dalhousie University Halifax, Nova Scotia, Canada B3H 3J5 aut Erdélyi Tamás Department of Mathematics, The Ohio State University 231 West Eighteenth Avenue, Columbus, Ohio 43210, USA aut Journal of the London Mathematical Society Oxford University Press 51/3(1995-06), 573-588 0024-6107 51:3<573 1995 51 jlms https://doi.org/10.1112/jlms/51.3.573 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1112/jlms/51.3.573 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Borwein Peter Department of Mathematics, Dalhousie University Halifax, Nova Scotia, Canada B3H 3J5 aut NATIONALLICENCE 700 1- Erdélyi Tamás Department of Mathematics, The Ohio State University 231 West Eighteenth Avenue, Columbus, Ohio 43210, USA aut NATIONALLICENCE 773 0- Journal of the London Mathematical Society Oxford University Press 51/3(1995-06), 573-588 0024-6107 51:3<573 1995 51 jlms Metadata rights reserved CC BY-NC-4.0 http://creativecommons.org/licenses/by-nc/4.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-oxford