Journal of Inequalities and Applications
Volume 4 (1999), Issue 4, Pages 327-338

Landau and Kolmogoroff type polynomial inequalities

Claudia R. R. Alves and Dimitar K. Dimitrov

Departamento de Ciências de Computação e Estatística, IBILCE, Universidade Estadual Paulista, São José do Rio Preto 15054-000, SP, Brazil

Received 4 December 1998; Revised 2 February 1999

Copyright © 1999 Claudia R. R. Alves and Dimitar K. Dimitrov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let 0<j<mn be integers. Denote by the norm f2=f2(x)exp(x2)dx. For various positive values of A and B we establish Kolmogoroff type inequalities f(j)2Af(m)+BfAθk+Bμk, with certain constants θkeμk, which hold for every fπn (πn denotes the space of real algebraic polynomials of degree not exceeding n).

For the particular case j=1 and m=2, we provide a complete characterisation of the positive constants A and B, for which the corresponding Landau type polynomial inequalities f2Af+BfAθk+Bμk, hold. In each case we determine the corresponding extremal polynomials for which equal- ities are attained.