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Some Zygmund type Lq inequalities for polynomials

โœ Scribed by A. Aziz; N.A. Rather

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
215 KB
Volume
289
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

Let p(z) be a polynomial of degree n which does not vanish in |z| < k. It is known that for each q > 0 and k 1,

In this paper, we present a refinement of this inequality which besides yielding some interesting results as corollaries, includes some well-known results as special cases. We also consider an analogous problem for the class of polynomials p(z) = a n z n + n ฮฝ=m a n-ฮฝ z n-ฮฝ not vanishing outside the disk |z| k, where k 1 and obtain a sharp result.

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