## Search

Now showing items 11-20 of 35

#### 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.

#### 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 [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 ...

#### 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.

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

(Journal article; Peer reviewed; Tidsskriftartikkel, 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; Tidsskriftartikkel, 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).

#### A new look at classical inequalities involving Banach lattice norms

(Journal article; Peer reviewed; Tidsskriftartikkel, 2017-12-08)

Some classical inequalities are known also in a more general form of Banach lattice norms and/or in continuous forms (i.e., for ‘continuous’ many functions are involved instead of finite many as in the classical situation). The main aim of this paper is to initiate a more consequent study of classical inequalities in this more general frame. We already here contribute by discussing some results of ...

#### Additive weighted Lp estimates of some classes of integral operators involving generalized Oinarov kernels

(Journal article; Peer reviewed; Tidsskriftartikkel, 2017)

#### Geometric Construction of Some Lehmer Means

(Journal article; Tidsskriftartikkel; Peer reviewed, 2018-11-14)

The main aim of this paper is to contribute to the recently initiated research concerning geometric constructions of means, where the variables are appearing as line segments. The present study shows that all Lehmer means of two variables for integer power k and for k = m 2 , where m is an integer, can be geometrically constructed, that Lehmer means for power k = 0,1 and 2 can be geometrically ...