$L_p$ inequalities for the growth of polynomials with restricted zeros

Rather, Nisar A., Gulzar, Suhail, and Bhat, Aijaz A.. "$L_{p}$ inequalities for the growth of polynomials with restricted zeros." Archivum Mathematicum 058.3 (2022): 159-167. <http://eudml.org/doc/298353>.

@article{Rather2022,
abstract = {Let $P(z)=\sum _\{\nu =0\}^\{n\}a_\{\nu \}z^\{\nu \}$ be a polynomial of degree at most $n$ which does not vanish in the disk $|z|<1$, then for $1\le p<\infty $ and $R>1$, Boas and Rahman proved \[\left\Vert P(Rz)\right\Vert \_\{p\}\le \big (\left\Vert R^\{n\}+z\right\Vert \_\{p\}/\left\Vert 1+z\right\Vert \_\{p\}\big )\left\Vert P\right\Vert \_\{p\}.\] In this paper, we improve the above inequality for $0\le p < \infty $ by involving some of the coefficients of the polynomial $P(z)$. Analogous result for the class of polynomials $P(z)$ having no zero in $|z|>1$ is also given.},
author = {Rather, Nisar A., Gulzar, Suhail, Bhat, Aijaz A.},
journal = {Archivum Mathematicum},
keywords = {polynomials; integral inequalities; complex domain},
language = {eng},
number = {3},
pages = {159-167},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {$L_\{p\}$ inequalities for the growth of polynomials with restricted zeros},
url = {http://eudml.org/doc/298353},
volume = {058},
year = {2022},
}

TY - JOUR
AU - Rather, Nisar A.
AU - Gulzar, Suhail
AU - Bhat, Aijaz A.
TI - $L_{p}$ inequalities for the growth of polynomials with restricted zeros
JO - Archivum Mathematicum
PY - 2022
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 058
IS - 3
SP - 159
EP - 167
AB - Let $P(z)=\sum _{\nu =0}^{n}a_{\nu }z^{\nu }$ be a polynomial of degree at most $n$ which does not vanish in the disk $|z|<1$, then for $1\le p<\infty $ and $R>1$, Boas and Rahman proved \[\left\Vert P(Rz)\right\Vert _{p}\le \big (\left\Vert R^{n}+z\right\Vert _{p}/\left\Vert 1+z\right\Vert _{p}\big )\left\Vert P\right\Vert _{p}.\] In this paper, we improve the above inequality for $0\le p < \infty $ by involving some of the coefficients of the polynomial $P(z)$. Analogous result for the class of polynomials $P(z)$ having no zero in $|z|>1$ is also given.
LA - eng
KW - polynomials; integral inequalities; complex domain
UR - http://eudml.org/doc/298353
ER -