Some L_p Inequalities for B-Operators

Nisar Ahmad Rather, Sajad Hussain Ahangar

Department of mathematics, University of Kashmir, Harzarbal, Sringar, India..

DOI: 10.4236/am.2013.41026                

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 every R≧1, p ≧ 1, where B is a B_n-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.

Keywords

L^p -Inequalities; B_n-Operators; Polynomials

Conflicts of Interest

The authors declare no conflicts of interest.

References

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