On some inequalities involving the zeros and weighted \(L^p\) norms of polynomials (Q2750886)
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scientific article; zbMATH DE number 1663131
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On some inequalities involving the zeros and weighted \(L^p\) norms of polynomials |
scientific article; zbMATH DE number 1663131 |
Statements
21 October 2001
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inequalities
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zeros
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weighted \(L^p\) norms
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polynomial
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On some inequalities involving the zeros and weighted \(L^p\) norms of polynomials (English)
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Using Parseval's identity and the Hardy-Littlewood-Pólya inequality on the maximal decreasing rearrangement, the author establishes some sharp inequalities involving the weighted \(L^p\) norm and the zeros of polynomials. This enables the author to generalise an inequality proved earlier by \textit{A. Kroó} and \textit{I. Pritsker} [Bull. Lond. Math. Soc. 31, No.~3, 269-278 (1999; Zbl 0929.30005), Theorem 2.4].
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