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Some new iterated Hardy-type inequalities: the case theta=1
(Journal article; Tidsskriftartikkel; Peer reviewed, 2013-11-08)
In this paper we characterize the validity of the Hardy-type inequality ∥ ∥ ∫ <sub>s</sub>∞) h(z)dz ∥ p,u,(0,t) ∥ q,w,(=,∞≤ c∥h∥ 1,v(0,∞) where 0 < p < ∞,0< q ≤ +∞, u, w and v are weight functions on (0,∞). It is pointed
out that this characterization can be used to obtain new characterizations for the
boundedness between weighted Lebesgue spaces ...
Sharp Hp-Lp type inequalities of weighted maximal operators of Vilenkin-Nörlund means and its applications
(Peer reviewed; Journal article; Tidsskriftsartikkel, 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.
Weighted Hardy type inequalities for supremum operators on the cones of monotone functions
(Peer reviewed; Journal article; Tidsskriftsartikkel, 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 new estimates of the ‘Jensen gap’
(Peer reviewed; Journal article; Tidsskriftsartikkel, 2016-02-01)
Some new Hardy-type inequalities in q-analysis
(Peer reviewed; Journal article; Tidsskriftsartikkel, 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.
Some sharp inequalities for integral operators with homogeneous kernel
(Peer reviewed; Journal article; Tidsskriftsartikkel, 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 for Riemann-Liouville fractional q-integral operator
(Peer reviewed; Journal article; Tidsskriftsartikkel, 2015-09-24)
We consider the q-analog of the Riemann-Liouville fractional q-integral operator of order n∈Nn∈N. Some new Hardy-type inequalities for this operator are proved and discussed.
A note on the maximal operators of Vilenkin-Nörlund means with non-increasing coefficients
(Peer reviewed; Journal article; Tidsskriftsartikkel, 2016)
In [14] 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 [14], and so ...
Time scale Hardy-type inequalities with ‘broken’ exponent p
(Peer reviewed; Journal article; Tidsskriftsartikkel, 2015-01-16)
In this paper, some new Hardy-type inequalities involving ?broken? exponents are
derived on arbitrary time scales. Our approach uses both convexity and
superquadracity arguments, and the results obtained generalize, complement and
provide refinements of some known results in literature
A new discrete Hardy-type inequality with kernels and monotone functions
(Peer reviewed; Journal article; Tidsskriftartikkel, 2015-10-06)
A new discrete Hardy-type inequality with kernels and monotone functions is proved for the case 1<q<p<∞1<q<p<∞. This result is discussed in a general framework and some applications related to Hölder’s summation method are pointed out.