Now showing items 1-7 of 7
Some new estimates of the ‘Jensen gap’
(Peer reviewed, 2016-02-01)
Weighted Hardy type inequalities for supremum operators on the cones of monotone functions
(Peer reviewed, 2016-09-28)
The complete characterization of the weighted L<sup>p</sup>-L<sup>r</sup> inequalities of supremum operators on the cones of monotone functions for all 0 < p, r≤∞ is given.
Some sharp inequalities for integral operators with homogeneous kernel
(Peer reviewed, 2016-04-09)
One goal of this paper is to show that a big number of inequalities for functions in Lp(R+), p ≥ 1, proved from time to time in journal publications are particular cases of some known general results for integral operators with homogeneous kernels including, in particular, the statements on sharp constants. Some new results are also included, e.g. the similar general equivalence result is proved and ...
Some new Hardy-type inequalities in q-analysis
(Peer reviewed, 2016-09)
We derive necessary and sufficient conditions (of Muckenhoupt-Bradley type) for the validity of q -analogs of (r, p) -weighted Hardy-type inequalities for all possible positive values of the parameters r and p . We also point out some possibilities to further develop the theory of Hardy-type inequalities in this new direction.
A note on the maximal operators of Vilenkin-Nörlund means with non-increasing coefficients
(Peer reviewed, 2016)
In  we investigated some Vilenkin—Nörlund means with non-increasing coefficients. In particular, it was proved that under some special conditions the maximal operators of such summabily methods are bounded from the Hardy space H1/(1+α) to the space weak-L1/(1+α), (0 < α ≦ 1). In this paper we construct a martingale in the space H1/(1+α), which satisfies the conditions considered in , and so ...
Sharp Hp-Lp type inequalities of weighted maximal operators of Vilenkin-Nörlund means and its applications
(Peer reviewed, 2016-10-01)
We prove and discuss some new Hp-Lp type inequalities of weighted maximal operators of Vilenkin-Nörlund means with monotone coefficients. It is also proved that these inequalities are the best possible in a special sense. We also apply these results to prove strong summability for such Vilenkin-Nörlund means. As applications, both some well-known and new results are pointed out.
Boundedness and compactness of a class of Hardy type operators
(Journal article; Tidsskriftartikkel; Peer reviewed, 2016-12-13)
We establish characterizations of both boundedness and of compactness of a general class of fractional integral operators involving the Riemann-Liouville, Hadamard, and Erdelyi-Kober operators. In particular, these results imply new results in the theory of Hardy type inequalities. As applications both new and well-known results are pointed out.