In this paper, we reconstruct the Hardy-Littlewood’s inequality byusing the method of the weight coefficient and the technic of real analysis includinga best constant factor. An open problem is raised.

By using the way of weight coefficients, the technique of real analysis, and Hermite-Hadamard's inequality, a more accurate Hardy-Mulholland-type inequality with multi-parameters and a best possible constant factor is given. The equivalent forms, the reverses, the operator expressions and some particular cases are considered.

By means of the weight functions, the technique of real analysis and Hermite-Hadamard's inequality, a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of logarithmic function and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions, the reverses and some particular cases are also considered.

In this paper it is shown that a new Hardy-Hilbert type integral inequality can be established by introducing a proper integral kernel function, and that the constant factor is proved to be the best possible. In particular, for case p = 2, a new Hilbert type integral inequality is given .And as the mathematics aesthetics, several important constants π and Euler number En appear simultaneously i...

Differential forms are interesting and important generalizations of real functions and distributions. Many interesting results and applications of differential forms have recently been found in some fields. As an important tool the Hardy-Littlewood inequality have been playing critical roles in many mathematics, including potential analysis, partial differential equations and the theory of elas...

One gets more than two hundred papers when searching by the keywords “Hardy” and “inequality” in the review journals Zentralblatt für Mathematik or Mathematical Reviews. Almost half of these publications appeared after 1990. In the absolute majority, these papers deal with various generalizations, extensions and improvements of the wellknown Hardy inequality (HI) presented in monograph [8] (bot...

We prove a Hardy-Littlewood type inequality with respect to a system called Vilenkin-like system (which is a common generalisation of several well-known systems ) in the two-dimensional case.