On sharp constants in Marcinkiewicz-Zygmund and Plancherel-Polya inequalities
نویسندگان
چکیده
منابع مشابه
On Sharp Constants in Marcinkiewicz-zygmund and Plancherel-polya Inequalities
The Plancherel-Polya inequalities assert that for 1 < p <∞, and entire functions f of exponential type at most π, Ap ∞ ∑ j=−∞ |f (j)| ≤ ∫ ∞ −∞ |f | ≤ Bp ∞ ∑ j=−∞ |f (j)| . The Marcinkiewicz-Zygmund inequalities assert that for n ≥ 1, and polynomials P of degree ≤ n− 1, Ap n n ∑ j=1 ∣∣∣P (e2πij/n)∣∣∣p ≤ ∫ 1 0 ∣∣P (e2πit)∣∣p dt ≤ B′ p n n ∑ j=1 ∣∣∣P (e2πij/n)∣∣∣p . We show that the sharp constant...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2014
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2014-12270-2