Marcinkiewicz-Zygmund inequalities
نویسندگان
چکیده
We study a generalization of the classical Marcinkiewicz-Zygmund inequalities. We relate this problem to the sampling sequences in the Paley-Wiener space and by using this analogy we give sharp necessary and sufficient computable conditions for a family of points to satisfy the Marcinkiewicz-Zygmund inequalities.
منابع مشابه
On Marcinkiewicz-Zygmund-Type Inequalities
We investigate the relationships between the Marcinkiewicz-Zygmund-type inequalities and certain shifted average operators. Applications to the mean boundedness of a quasi-interpolatory operator in the case of trigonometric polynomials, Jacobi polynomials, and Freud polynomials are presented.
متن کاملOn Marcinkiewicz-zygmund Inequalities at Jacobi Zeros and Their Bessel Function Cousins
Marcinkiewicz-Zygmund Inequalities involving the zeros {xkn} of Jacobi polynomials for the weight wα,β can take the form
متن کامل2 Joaquim Ortega - Cerdà and Jordi
We study a generalization of the classical Marcinkiewicz-Zygmund inequalities. We relate this problem to the sampling sequences in the Paley-Wiener space and by using this analogy we give sharp necessary and sufficient computable conditions for a family of points to satisfy the Marcinkiewicz-Zygmund inequalities.
متن کاملOn Converse Marcinkiewicz-zygmund Inequalities
We obtain converse Marcinkiewicz-Zygmund inequalities such as k P kLp[ 1;1] C 0@ n X j=1 j jP (tj)j 1A1=p for polynomials P of degree n 1, under general conditions on the points ftjgj=1 and on the function . The weights f jgj=1 are appropriately chosen. We illustrate the results by applying them to extended Lagrange interpolation for exponential weights on [ 1; 1].
متن کاملOn 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Journal of Approximation Theory
دوره 145 شماره
صفحات -
تاریخ انتشار 2007