Hardy-type Inequalities on the Real Line
نویسنده
چکیده
We prove a certain type of inequalities concerning the integral of the Fourier transform of a function integrable on the real line.
منابع مشابه
A Study of the Real Hardy Inequality
We show that some Hardy-type inequalities on the circle can be proved to be true on the real line. Namely, we discuss the idea of getting Hardy inequalities on the real line by the use of corresponding inequalities on the circle. In the last section, we prove the truth of a certain open problem under some restrictions.
متن کاملGeneral Hardy-Type Inequalities with Non-conjugate Exponents
We derive whole series of new integral inequalities of the Hardy-type, with non-conjugate exponents. First, we prove and discuss two equivalent general inequa-li-ties of such type, as well as their corresponding reverse inequalities. General results are then applied to special Hardy-type kernel and power weights. Also, some estimates of weight functions and constant factors are obtained. ...
متن کاملOn a decomposition of Hardy--Hilbert's type inequality
In this paper, two pairs of new inequalities are given, which decompose two Hilbert-type inequalities.
متن کاملSome inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm
Let A = (an;k)n;k1 and B = (bn;k)n;k1 be two non-negative ma-trices. Denote by Lv;p;q;B(A), the supremum of those L, satisfying the followinginequality:k Ax kv;B(q) L k x kv;B(p);where x 0 and x 2 lp(v;B) and also v = (vn)1n=1 is an increasing, non-negativesequence of real numbers. In this paper, we obtain a Hardy-type formula forLv;p;q;B(H), where H is the Hausdor matrix and 0 < q p 1. Also...
متن کاملSome functional inequalities in variable exponent spaces with a more generalization of uniform continuity condition
Some functional inequalities in variable exponent Lebesgue spaces are presented. The bi-weighted modular inequality with variable exponent $p(.)$ for the Hardy operator restricted to non- increasing function which is$$int_0^infty (frac{1}{x}int_0^x f(t)dt)^{p(x)}v(x)dxleqCint_0^infty f(x)^{p(x)}u(x)dx,$$ is studied. We show that the exponent $p(.)$ for which these modular ine...
متن کامل