Some Lp Inequalities for the Polar Deriv
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N.K Govil; Griffith Nyuydinkong; Berhanu Tameru
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Article
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2001
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Elsevier Science
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English
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Let p n z be a polynomial of degree n and D ฮฑ p n z its polar derivative. It has been proved that if p n z has no zeros in z < 1, then for ฮด โฅ 1 and ฮฑ โฅ 1, 2ฯ 0 D ฮฑ p n e iฮธ ฮด dฮธ 1/ฮด โค n ฮฑ + 1 F ฮด 2ฯ 0 p n e iฮธ ฮด dฮธ 1/ฮด where F ฮด = 2ฯ/ 2ฯ 0 1 + e iฮธ ฮด dฮธ 1/ฮด . We also obtain analogous inequalities