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Now showing items 1-9 of 9

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

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

#### Weighted Hardy Operators in Complementary Morrey Spaces

(Journal article; Tidsskriftartikkel; Peer reviewed, 2012)

#### 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 ...

#### 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 ...

#### 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 ...

#### On geometric construction of some power means

(Journal article; Peer reviewed, 2018-11-27)

In the homogenization theory, there are many examples where the effective conductivities of composite structures are power means of the local conductivities. The main aim of this paper is to initiate research concerning geometric construction of some power means of three or more variables. We contribute by giving methods for the geometric construction of the harmonic mean $ P_{-1} $ and the arithmetic ...

#### A New Look at the Single Ladder Problem (SLP) via Integer Parametric Solutions to the Corresponding Quartic Equation

(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-02-18)

The aim is to put new light on the single ladder problem (SLP). Some new methods for finding complete integer solutions to the corresponding quartic equation
z
4
−2L
z
3
+(
L
2
−
a
2
−
b
2
)
z
2
+2L
a
2
z−
L
2
a
2
=0
z4−2Lz3+(L2−a2−b2)z2+2La2z−L2a2=0
are developed. For the case
L≥
L
min
L≥Lmin
, these methods imply a complete parametric representation for integer ...

#### Some new Fourier inequalities for unbounded orthogonal systems in Lorentz-Zygmund spaces

(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-03-20)

In this paper we prove some essential complements of the paper (J. Inequal. Appl. 2019:171, 2019) on the same theme. We prove some new Fourier inequalities in the case of the Lorentz–Zygmund function spaces
L
q,r
(logL
)
α
Lq,r(logL)α
involved and in the case with an unbounded orthonormal system. More exactly, in this paper we prove and discuss some new Fourier inequalities of this type for ...

#### Some inequalities related to strong convergence of Riesz logarithmic means

(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-03-23)

In this paper we derive a new strong convergence theorem of Riesz logarithmic means of the one-dimensional Vilenkin–Fourier (Walsh–Fourier) series. The corresponding inequality is pointed out and it is also proved that the inequality is in a sense sharp, at least for the case with Walsh–Fourier series.