Open AccessSome <i>L<sub>p</sub></i> Inequalities for <i>B</i>-Operators
Author(s) -
N. A. Rather,
S. H. Ahangar
Publication year - 2013
Publication title -
applied mathematics
Language(s) - English
Resource type - Journals
eISSN - 2152-7393
pISSN - 2152-7385
DOI - 10.4236/am.2013.41026
Subject(s) - ampere , mathematics , operator (biology) , combinatorics , chemistry , physics , biochemistry , quantum mechanics , repressor , voltage , transcription factor , gene
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 every R≧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≦p1 as well.
, 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 every R≧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≦p1 as well.