Pointwise Remez- and Nikolskii-type Inequalities for Exponential Sums
نویسندگان
چکیده
Let
منابع مشابه
Weighted inequalities for generalized polynomials with doubling weights
Many weighted polynomial inequalities, such as the Bernstein, Marcinkiewicz, Schur, Remez, Nikolskii inequalities, with doubling weights were proved by Mastroianni and Totik for the case [Formula: see text], and by Tamás Erdélyi for [Formula: see text]. In this paper we extend such polynomial inequalities to those for generalized trigonometric polynomials. We also prove the large sieve for gene...
متن کاملMarkov-bernstein Type Inequality for Trigonometric Polynomials with Respect to Doubling Weights on [−ω, Ω]
Various important weighted polynomial inequalities, such as Bernstein, Marcinkiewicz, Nikolskii, Schur, Remez, etc. inequalities, have been proved recently by Giuseppe Mastroianni and Vilmos Totik under minimal assumptions on the weights. In most of the cases this minimal assumption is the doubling condition. Here, based on a recently proved Bernstein-type inequality by D.S. Lubinsky, we establ...
متن کاملRemez-type Inequalities on the Size of Generalized Polynomials
Generalized polynomials are defined as products of polynomials raised to positive real powers. The generalized degree can be defined in a natural way. A number of classical inequalities holding for polynomials can be extended for generalized polynomials utilizing the generalized degree in place of the ordinary one. Remez established a sharp upper bound for the maximum modulus on [— 1,1] of alge...
متن کاملAsymptotic Behavior of Nikolskii Constants for Polynomials on the Unit Circle
Let q > p > 0, and consider the Nikolskii constants Λn,p,q = inf deg(P )≤n−1 ‖P‖p ‖P‖q , where the norm is with respect to normalized Lebesgue measure on the unit circle. We prove that lim sup n→∞ n 1 p − 1 q Λp,q ≤ Ep,q , where Ep,q = inf ‖f‖Lp(R) ‖f‖Lq(R) , and the inf is taken over all entire functions f of exponential type at most π. We conjecture that the lim sup can be replaced by a limit...
متن کاملNorming Sets and Related Remez-type Inequalities
The classical Remez inequality ([33]) bounds the maximum of the absolute value of a real polynomial P of degree d on [−1, 1] through the maximum of its absolute value on any subset Z ⊂ [−1, 1] of positive Lebesgue measure. Extensions to several variables and to certain sets of Lebesgue measure zero, massive in a much weaker sense, are available (see, e.g., [14, 39, 8]). Still, given a subset Z ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999