Abstract We consider the Hilbert-type operator defined by $$\begin{aligned} H_{\omega }(f)(z)=\int _0^1 f(t)\left( \frac{1}{z}\int _0^z B^{\omega }_t(u)\,du\right) \,\omega (t)dt, \end{aligned}$$ H ω ( f ...

The first power weighted version of Hardy's inequality can be rewritten as [Formula: see text] where the constant [Formula: see text] is sharp. This inequality holds in the reversed direction when [Formula: see text]. In this paper we prove and discuss some discrete analogues of Hardy-type inequalities in fractional h-discrete calculus. Moreover, we prove that the corresponding constants are sh...

A new approach to boundary trace inequalities for Sobolev functions is presented, which reduces any trace inequality involving general rearrangement-invariant norms to an equivalent, considerably simpler, one-dimensional inequality for a Hardy-type operator. In particular, improvements of classical boundary trace embeddings and new optimal trace embeddings are derived.

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.

The main objective of this paper is some new special Hilbert-type and HardyHilbert-type inequalities in (R) with k ≥ 2 non-conjugate parameters which are obtained by using the well known Selberg’s integral formula for fractional integrals in an appropriate form. In such a way we obtain extensions over the whole set of real numbers, of some earlier results, previously known from the literature, ...

In this paper, we study the Schrödinger-Robertson uncertainty relations as corollaries of equalities in a scalar product space. Moreover, we give a number of characterizations in the case where the associated inequalities are in fact equalities. Our presentation is based exclusively on an algebraic observation on the standard Cauchy-Schwarz inequality and could presumably provide a clear and ex...

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...