Abstract By the use of weight coefficients, idea introduced parameters and technique real analysis, a more accurate Hilbert-type inequality in whole plane with general homogeneous kernel is given, which an extension Hardy–Hilbert’s inequality. An equivalent form obtained. The statements best possible constant factor related to several parameters, operator expressions few particular cases are co...

[1] G. H. HARDY, J. E. LITTLEWOOD AND G. POLYA, Inequalities, Cambridge Univ. Press, Cambridge, 1995. [2] GAO MINGZHE, A Note on the Hardy-Hilbert Inequality, J. Math. Anal. Appl. Vol. 204, No. 1 (1996), 346–351. [3] GAO MINGZHE AND YANG BICHEN, on the Extended Hilbert’s Inequality, Proc. Amer. Math. Soc. Vol. 126, No. 3 (1998), 751–759. [4] W. H. GREUB, Linear Algebra, Springer Verlag, Berlin,...

Abstract By means of the weight functions, idea introducing parameters and technique real analysis, a new Hardy–Hilbert-type integral inequality with homogeneous kernel $\frac{1}{(x + y)^{\lambda}}\ (\lambda &gt; 0)$ 1(x+y<m...

In this paper, we address Hardy–Hilbert-type inequality by virtue of constructing weight coefficients and introducing parameters. By using the Euler–Maclaurin summation formula, Abel’s partial differential mean value theorem, a new weighted containing two sums can be proven, which is further generalization an existing result. Based on obtained results, provide equivalent statements best possibl...

We study various inequalities for numerical radius and Berezin number of a bounded linear operator on Hilbert space. It is proved that the pure two-isometry 1 Crawford 0. In particular, we show any scalar-valued non-constant inner function θ, Toeplitz Tθ Hardy space 0, respectively. also shown multiplicative class isometries sub-multiplicative commutants shift. have illustrated these results wi...

In a generalization of the classical Hilbert inequality by Hardy, Littlewood and Pólya, the best constant for an inequality is determined provided that the generating function for the corresponding matrix satisfies certain monotonicity condition. In this paper, we determine the best constant for a class of inequalities when the monotonicity condition is no longer satisfied. Mathematics subject ...

We explore a variety of pleasing connections between analysis, number theory and operator theory, while revisiting a number of beautiful inequalities originating with Hilbert, Hardy and others. We shall first establish the aforementioned Hilbert inequality [?, ?] and then apply it to various multiple zeta values. In consequence we obtain the norm of the classical Hilbert matrix, while illustrat...