Lp inequalities for polynomials with restricted zeros

@article{Aziz1998LpIF,
  title={Lp inequalities for polynomials with restricted zeros},
  author={Abdul Aziz and Wali Mohammad Shah},
  journal={Proceedings Mathematical Sciences},
  year={1998},
  volume={108},
  pages={63-68}
}
AbstractLetP(z) be a polynomial of degreen which does not vanish in the disk |z|0 andk≥1, $$\begin{gathered} \left\{ {\frac{1}{{2\pi }}\int_0^{2\pi } {\left| {P^{(s)} (e^{i\theta } )} \right|^p d\theta } } \right\}^{1/p} \leqslant n(n - 1) \cdots (n - s + 1) B_p \hfill \\ \times \left\{ {\frac{1}{{2\pi }}\int_0^{2\pi } {\left| {P(e^{i\theta } )} \right|^p d\theta } } \right\}^{1/p} , \hfill \\ \end{gathered} $$ where $$B_p = \left\{ {\frac{1}{{2\pi }}\int_0^{2\pi } {\left| {k^s + e^{i\alpha… CONTINUE READING

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