in this paper, two pairs of new inequalities are given, which decompose two hilbert-type inequalities.

Let H(S) be the Hardy space on the unit sphere S in C. We establish a local inequality for Hankel operators Hf = (1 − P )Mf |H(S). As an application of this local inequality, we characterize the membership of Hf in the Lorentz-like ideal C p , 2n < p <∞.

In this paper, a new inequality for the weight coefficient w(q, n) in the form sin(r/p) 2mi/p + n_i/q q > I,+ I, 6 N P q is proved. This is followed by a strengthened version ofthe Hardy-I-lilben inequality.

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 ...

In 2012, W. T. Sulaiman presented new kinds of Hardy’s integral inequalities. In this paper, we derive some new extensions of the famous Hardy’s integral inequality. The results present direct generalization of the original Hardy inequality. In addition, the corresponding reverse relation is also obtained.

Abstract. The main result includes features of a Hardy-type inequality and an inequality of either Sobolev or Gagliardo-Nirenberg type. It is inspired by the method of proof of a recent improved Sobolev inequality derived by M. Ledoux which brings out the connection between Sobolev embeddings and heat kernel bounds. Here Ledoux’s technique is applied to the operator L := x · ∇ and the analysis ...

By means of weight functions and Hermite-Hadamard's inequality, and introducing a discrete interval variable, a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of arc tangent function and a best possible constant factor is given, which is an extension of a published result. The equivalent forms and the operator expressions are also considered.

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...

We show that the sharp constant in the Hardy-Littlewood-Sobolev inequality can be derived using the method that we employed earlier for a similar inequality on the Heisenberg group. The merit of this proof is that it does not rely on rearrangement inequalities; it is the first one to do so for the whole parameter range.