An extension of a multidimensional Hilbert-type inequality

An extended multidimensional Hardy-Hilbert-type inequality with a general homogeneous kernel

In this paper, by the use of the weight coefficients, the transfer formula and the technique of real analysis, an extended multidimensional Hardy-Hilbert-type inequality with a general homogeneous kernel and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions and a few examples are considered.

A multidimensional discrete Hilbert-type inequality

In this paper, by using the way of weight coecients and technique of real analysis, a multidimensionaldiscrete Hilbert-type inequality with a best possible constant factor is given. The equivalentform, the operator expression with the norm are considered.

An Operator Extension of Bohr's inequality

On a New Reverse Hilbert\'s Type Inequality

In this paper, by using the Euler-Maclaurin expansion for the Riemann-$zeta$ function, we establish an inequality of a weight coefficient. Using this inequality, we derive a new reverse Hilbert's type inequality. As an applications, an equivalent form is obtained.

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...