The main objective of this paper is to deduce Hilbert-Pachpatte type inequalities using Bonsall’s form of Hilbert’s and Hardy-Hilbert’s inequalities, both in discrete and continuous case.

By the use of the transfer formula, the methods of weight functions and technique of Real Analysis, a multidimensional Hilbert-type integral inequality with a few parameters and a best possible constant factor related to the kernel of logarithm function is given. The equivalent forms and some reverses are obtained. The operator expressions and a few particular results related to the kernels of ...

By using the way of weight functions and technique of real analysis, a new multiple half-discrete Hilbert-type inequality with the best constant factor is given. As applications, the equivalent forms, operator expressions as well as some reverse inequalities are also considered. Mathematics subject classification (2010): 26D15, 47A07.

In the paper, by using the way of weight functions and the theory of operators, a Hilbert-type integral operator with the homogeneous kernel of −λ-degree and its norm are considered. As for applications, two equivalent inequalities with the best constant factors and some particular norms are obtained.

In this paper, by the use of weight coefficients, the transfer formula and the technique of real analysis, a new multidimensional Hilbert-type inequality with multi-parameters and a best possible constant factor is given, which is an extension of some published results. Moreover, the equivalent forms, the operator expressions and a few particular inequalities are considered.

In this paper, by using some classical Mulholland type inequality, Berezin symbols and reproducing kernel technique, we prove the power inequalities for number $ber(A)$ self-adjoint operators $A$ on ${H}(\Omega )$. Namely, inequality Hilbert space are established. By applying that $(ber(A))^{n}\leq C_{1}ber(A^{n})$ any positive operator