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#### Weighted Hardy-Type Inequalities in Variable Exponent Morrey-Type Spaces

(Journal article; Peer reviewed, 2013)

We study the p(.) -> q(.) boundedness of weighted multidimensional Hardy-type operators H-w(alpha(.)) and H-w(alpha(.)) of variable order alpha(x), with radial weight w(vertical bar x vertical bar), from a variable exponent locally generalized Morrey space L-p(.),L-phi(.)(R-n, w) to another L-q(.),L-psi(.)(R-n, w). The exponents are assumed to satisfy the decay condition at the origin and infinity. ...

#### 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 ...

#### 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.

#### Time scale Hardy-type inequalities with ‘broken’ exponent p

(Peer reviewed, 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

#### Some new Hardy-type inequalities for Riemann-Liouville fractional q-integral operator

(Peer reviewed, 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 new discrete Hardy-type inequality with kernels and monotone functions

(Peer reviewed, 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.

#### A note on the maximal operators of Vilenkin-Nörlund means with non-increasing coefficients

(Peer reviewed, 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 ...

#### 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.

#### Fejér and Hermite-Hadamard Type Inequalities for N-Quasiconvex Functions

(Journal article; Peer reviewed, 2017-12-28)

Some new extensions and re finements of Hermite – Hadamard and Fejer type inequalities for functions which are N -quasiconvex are derived and discussed.

#### Some new Two-Sided Inequalities concerning the Fourier Transform

(Journal article; Peer reviewed, 2017)

The classical Hausdorff-Young and Hardy-Littlewood-Stein inequalities do not hold for p > 2. In this paper we prove that if we restrict to net spaces we can even derive a two-sided estimate for all p > 1. In particular, this result generalizes a recent result by Liflyand E. and Tikhonov S. [7] (MR 2464253).