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#### 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

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

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

#### 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 ...

#### Multi-dimensional Hardy type inequalities in Hölder spaces

(Journal article; Tidsskriftartikkel; Peer reviewed, 2018)

Most Hardy type inequalities concern boundedness of the Hardy type operators in Lebesgue spaces. In this paper we prove some new multi-dimensional Hardy type inequalities in Hölder spaces.

#### Hardy-type inequalities in fractional h-discrete calculus

(Journal article; Tidsskriftartikkel; Peer reviewed, 2018-04-04)

The first power weighted version of Hardy’s inequality can be rewritten as [<i>mathematical formula</i>] where the constant <i>C</i> =[<i>p</i> / <i>p</i> - <i><b>a</b></i> - 1]<sup><i>p</i></sup> is sharp. This inequality holds in the reversed direction when<math xmlns="http://www.w3.org/1998/Math/MathML">
<mn>0</mn>
<mo>≤<!-- ≤ --></mo>
<mi><i>p</i></mi>
<mo><</mo>
<mn>1</mn>
...