A Hilbert's Inequality with a Best Constant Factor
نویسندگان
چکیده
منابع مشابه
A more accurate half-discrete Hardy-Hilbert-type inequality with the best possible constant factor related to the extended Riemann-Zeta function
By the method of weight coefficients, techniques of real analysis and Hermite-Hadamard's inequality, a half-discrete Hardy-Hilbert-type inequality related to the kernel of the hyperbolic cosecant function with the best possible constant factor expressed in terms of the extended Riemann-zeta function is proved. The more accurate equivalent forms, the operator expressions with the norm, the rever...
متن کاملBest Constant in Sobolev Inequality
The equality sign holds in (1) i] u has the Jorm: (3) u(x) = [a + btxI,~',-'] 1-~1~ , where Ix[ = (x~ @ ...-~x~) 1⁄2 and a, b are positive constants. Sobolev inequalities, also called Sobolev imbedding theorems, are very popular among writers in part ial differential equations or in the calculus of variations, and have been investigated by a great number of authors. Nevertheless there is a ques...
متن کاملFinding best possible constant for a polynomial inequality
Given a multi-variant polynomial inequality with a parameter, how to find the best possible value of this parameter that satisfies the inequality? For instance, find the greatest number k that satisfies a+b+c+k(ab+bc+ca)−(k+1)(ab+bc+ca) ≥ 0 for all nonnegative real numbers a, b, c. Analogues problems often appeared in studies of inequalities and were dealt with by various methods. In this paper...
متن کاملA Best Constant for Zygmund's Conjugate Function Inequality
When the space L log+L is given the Hardy-Littlewood norm the best constant in the corresponding version of Zygmund's conjugate function inequality is shown to be r2 3~2 + 5-2 7-2 + • ■ ■ K = I-2 + 3"2 + 5"2 + 7" This complements the recent result of Burgess Davis that the best constant in Kolmogorov's inequality is K"1. The symbol K will be used throughout for the constant p2 _ 3-2 + 5-2 _ 7-2...
متن کاملThe Best Constant in a Fractional Hardy Inequality
We prove an optimal Hardy inequality for the fractional Laplacian on the half-space. 1. Main result and discussion Let 0 < α < 2 and d = 1, 2, . . .. The purpose of this note is to prove the following Hardy-type inequality in the half-space D = {x = (x1, . . . , xd) ∈ R : xd > 0}. Theorem 1. For every u ∈ Cc(D), (1) 1 2 ∫
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2009
ISSN: 1029-242X
DOI: 10.1155/2009/820176