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Now showing items 1-10 of 29

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

(Journal article; Tidsskriftartikkel; 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. ...

#### Refinements of some limit hardy-Type Inequalities via Superquadracity

(Journal article; Tidsskriftartikkel; Peer reviewed, 2017-11-03)

Refinements of some limit Hardy-type inequalities are derived and discussed using the concept of superquadracity. We also proved that all three constants appearing in the refined inequalities obtained are sharp. The natural turning point of our refined Hardy inequality is p=2 and for this case we have even equality.

#### Some new estimates of the ‘Jensen gap’

(Peer reviewed, 2016-02-01)

#### Some inequalities for Cesàro means of double Vilenkin-Fourier series

(Journal article; Peer reviewed; Tidsskriftartikkel, 2018-12-19)

In this paper, we state and prove some new inequalities related to the rate of Lp approximation by Cesàro means of the quadratic partial sums of double Vilenkin–Fourier series of functions from Lp.

#### A NEW GENERALIZATION OF BOAS THEOREM FOR SOME LORENTZ SPACES Λq(ω)

(Journal article; Tidsskriftartikkel; Peer reviewed, 2018)

Let Λq( ω ), q > 0, denote the Lorentz space equipped with the (quasi) norm
[<i>MATHEMATICAL FORMULA</I>]
for a function f on [0,1] and with
ω
positive and equipped with some additional growth properties. A generalization of Boas theorem in the form of a two-sided inequality is obtained in the case of both general regular system [<i>MATHEMATICAL FORMULA</I>] and generalized Lorentz Λq( ω ) spaces

#### Weighted Hardy Operators in Complementary Morrey Spaces

(Journal article; Tidsskriftartikkel; Peer reviewed, 2012)

#### On Some Power Means and Their Geometric Constructions

(Journal article; Tidsskriftartikkel; Peer reviewed, 2018)

The main aim of this paper is to further develop the recently initiatedresearch concerning geometric construction of some power means wherethe variables are appearing as line segments. It will be demonstratedthat the arithmetic mean, the harmonic mean and the quadratic meancan be constructed for any number of variables and that all power meanswhere the number of variables are n = 2m, m 1 2 N for all ...

#### 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 ...

#### 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.