Hilbert-type Inequalities Research Articles

On Hilbert's type inequalities

By introducing two pairs of conjugate exponents and estimating the weight coefficients, we give generalizations of some Hilbert's type inequalities with the best constant factor. As applications, some particular results are considered.

On a Hilbert-Type Operator with a Symmetric Homogeneous Kernel of 1-Order and Applications

Some character of the symmetric homogenous kernel of 1-order in Hilbert-type operator is obtained. Two equivalent inequalities with the symmetric homogenous kernel of -order are given. As applications, some new Hilbert-type inequalities with the best constant factors and the equivalent forms as the particular cases are established.

On the Norm of a Self-Adjoint Operator and Applications to the Hilbert's Type Inequalities

On the Norm of a Self-Adjoint Operator and Applications to the Hilbert's Type Inequalities

On the norm of a Hilbert's type linear operator and applications

In this paper, the norm of a Hilbert's type linear operator T : l r → l r ( r > 1 ; r = p , q ) is given. As applications, a new operator inequality and the equivalent forms with the norm are obtained, and particularly some new extended Hilbert's type inequalities and the equivalent forms with the best constant factors are established.

Entire majorants via Euler–Maclaurin summation

It is the aim of this article to give extremal majorants of type 2 π δ 2\pi \delta for the class of functions f n ( x ) = sgn ( x ) x n f_n(x)=\text {sgn}(x)x^n , where n ∈ N n\in \mathbb {N} . As applications we obtain positive definite extensions to R \mathbb {R} of ± ( i t ) − m \pm (it)^{-m} defined on R ∖ [ − 1 , 1 ] \mathbb {R}\backslash [-1,1] , where m ∈ N m\in \mathbb {N} , optimal bounds in Hilbert-type inequalities for the class of functions ( i t ) − m (it)^{-m} , and majorants of type 2 π 2\pi for functions whose graphs are trapezoids.

On the norm of an integral operator and applications

In this paper, the norm of an integral operator T : L r ( 0 , ∞ ) → L r ( 0 , ∞ ) ( r > 1 ) is obtained. As applications, a new bilinear integral operator inequality with the norm and the equivalent forms are given, and some new Hilbert's type inequalities with the best constant factors as the particular cases are established.

Multiple Hilbert and Hardy-Hilbert inequalities with non-conjugate parameters

The main objective of this paper is a study of some new generalisations of Hilbert and Hardy-Hilbert type inequalities involving non-conjugate parameters. We prove general forms of multiple Hilbert-type inequalities, and we also introduce multiple inequalities of Hardy-Hilbert type with non-conjugate parameters.

Generalization of Hilbert and Hardy-Hilbert integral inequalities

The main objective of this paper is a study of some new generalizations of Hilbert's and Hardy-Hilbert's type inequalities. We establish general form of multiple Hilbert-type inequality and we also introduce multiple inequality of Hardy-Hilbert type. Further, the best possible constants are obtained for some general cases.

On the way of weight coefficient and research for the Hilbert-type inequalities

The Hilbert-type inequalities are certain significant weight inequalities, which play an important role in mathematical analysis and its applications. In this paper, we introduce the way of weight coefficient and consider its applications to the Hilbert-type inequalities. We will summarize how to use the way of weight coefficient to obtain some new improvements and generalizations of the Hilbert-type inequalities. Mathematics subject classification (2000): 26D15.