Hardy–Sobolev–type inequalities associated with the operator L := x · ∇ are established, using an improvement to the Sobolev embedding theorem obtained by M. Ledoux. The analysis involves the determination of the operator semigroup {e−tL∗L}t>0.

Let {cj} be a null sequence of bounded variation. We give appreciate smoothness and growth conditions on {cj} to obtain the pointwise convergence as well as Lr -convergence of Laguerre series ∑ cj a j . Then, we prove aHardy-Littlewood type inequality ∫∞ 0 |f(t)|r dt≤ C ∑∞ j=0 |cj| j̄1−r/2 for certain r ≤ 1, where f is the limit function of ∑ cj a j . Moreover, we show that if f(x) ∼ ∑cj a j is ...

We prove a certain type of inequalities concerning the integral of the Fourier transform of a function integrable on the real line.

In this paper some new Hardy–type inequalities on time scales are derived and proved using the concept of superquadratic functions. Also, we extend Hardy–type inequalities involving superquadratic functions with general kernels to the case with arbitrary time scales. Several consequences of our results are given and their connection with recent results in the literature are pointed out and disc...

We use a theorem of Cartlidge and the technique of Redheffer’s ”recurrent inequalities” to give some results on inequalities related to Hardy’s inequality.

*Correspondence: [email protected] 2Department of Construction and Information Engineering, Guangxi Modern Vocational Technology College, Hechi, Guangxi 547000, China Full list of author information is available at the end of the article Abstract We derive a strengthenment of a Hardy-Hilbert type inequality by using the Euler-Maclaurin expansion for the zeta function and estimating the weight...

By estimating a weight function, a reverse Hardy-Hilbert-type integral inequality with a best constant factor is obtained. As an application, some equivalent forms and some particular results have been established.

In this paper we prove some new results concerning multi-dimensional Hardy type integral inequalities and also some corresponding limit Pólya–Knopp type inequalities.