TITLE:
Some Lp Inequalities for B-Operators
AUTHORS:
Nisar Ahmad Rather, Sajad Hussain Ahangar
KEYWORDS:
Lp -Inequalities; Bn-Operators; Polynomials
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.1,
January
28,
2013
ABSTRACT: If P(z) is a polynomial of degree at most n having all its zeros in , then it was recently claimed by Shah and Liman ([1], estimates for the family of $B$-operators, Operators and Matrices, (2011), 79-87) that for everyR≧1, p ≧ 1, where B is a Bn-operator with parameters in the sense of Rahman [2], and . Unfortunately the proof of this result is not correct. In this paper, we present certain more general sharp Lp-inequalities for Bn-operators which not only provide a correct proof of the above inequality as a special case but also extend them for 0≦p﹤1 as well.