Some Lp Inequalities for B-Operators

DOI: 10.4236/am.2013.41026   PDF   HTML   XML   2,934 Downloads   4,467 Views   Citations

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 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 0p1 as well.

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N. Rather and S. Ahangar, "Some Lp Inequalities for B-Operators," Applied Mathematics, Vol. 4 No. 1, 2013, pp. 155-166. doi: 10.4236/am.2013.41026.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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