## Search

Now showing items 21-30 of 35

#### Boundedness and compactness of a class of Hardy type operators

(Journal article; Tidsskriftartikkel; Peer reviewed, 2016-12-13)

We establish characterizations of both boundedness and of compactness of a general
class of fractional integral operators involving the Riemann-Liouville, Hadamard, and
Erdelyi-Kober operators. In particular, these results imply new results in the theory of
Hardy type inequalities. As applications both new and well-known results are pointed
out.

#### Two-sided estimates of the Lebesgue constants with respect to Vilenkin systems and applications

(Journal article; Peer reviewed; Tidsskriftartikkel, 2017-03-13)

In this paper, we derive two-sided estimates of the Lebesgue constants for bounded Vilenkin systems, we also present some applications of importance, e.g., we obtain a characterization for the boundedness of a subsequence of partial sums with respect to Vilenkin–Fourier series of H 1 martingales in terms of n's variation. The conditions given in this paper are in a sense necessary and sufficient.

#### 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.

#### Potential type operators in PDEs and their applications

(Journal article; Peer reviewed; Tidsskriftartikkel, 2017-01)

We prove the boundedness of Potential operator in weighted generalized Morrey space in terms of Matuszewska-Orlicz indices of weights and apply this result to the Hemholtz equation in ℝ<sup>3</sup> with a free term in such a space. We also give a short overview of some typical situations when Potential type operators arise when solving PDEs.

#### 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>
...

#### A sharp boundedness result for restricted maximal operators of Vilenkin-Fourier series on martingale Hardy spaces

(Journal article; Peer reviewed, 2018-09-20)

The restricted maximal operators of partial sums with respect to bounded Vilenkin systems are investigated. We derive the maximal subspace of positive numbers, for which this operator is bounded from the Hardy space
H
p
to the Lebesgue space
L
p
for all
0<p≤1
. We also prove that the result is sharp in a particular sense.

#### 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 ...

#### Multidimensional Hardy-type inequalities on time scales with variable exponents

(Journal article; Peer reviewed, 2019)

A new Jensen inequality for multivariate superquadratic functions is derived and proved. The derived Jensen inequality is then employed to obtain the general Hardy-type integral inequality for superquadratic and subquadratic functions of several variables.

#### Equivalent integral conditions related to bilinear Hardy-type inequalities

(Journal article; Tidsskriftartikkel; Peer reviewed, 2019)

Inﬁnitely many, even scales of, equivalent conditions are derived to characterize the bilinear Hardy-type inequality under various ranges of parameters.

#### 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 ...