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Some Lp Inequalities for B-Operators

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DOI: 10.4236/am.2013.41026    2,719 Downloads   4,190 Views  

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

References

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