Søk
Viser treff 11-20 av 42
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.
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 ...
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-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. ...
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.
Hardy-type inequalities over balls in R^N for some bilinear and iterated operators
(Journal article; Tidsskriftartikkel; Peer reviewed, 2019)
Some new multidimensional Hardy-type inequalites are proved
and discussed. The cases with bilinear and iterated operators are considered
and some equivalence theorems are proved.
A New Development of the Classical Single Ladder Problem via Converting the Ladder to a Staircase
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-02-08)
Our purpose is to shed some new light on problems arising from a study of the classical
Single Ladder Problem (SLP). The basic idea is to convert the SLP to a corresponding Single Staircase
Problem. The main result (Theorem 1) shows that this idea works fine and new results can be
obtained by just calculating rational solutions of an algebraic equation. Some examples of such
concrete calculations ...
On the boundedness of subsequences of Vilenkin-Fejér means on the martingale Hardy spaces
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-03)
In this paper we characterize subsequences of Fejér means with respect to Vilenkin systems, which are bounded from the Hardy space <i>H<sub>p</sub></i> to the Lebesgue space <i>L<sub>p</sub></i>, for all 0 < p < 1/2. The result is in a sense sharp.
Rearrangements and jensen type inequalities related to convexity, superquadracity, strong convexity and 1-quasiconvexity
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-09)
In this paper we derive and discuss some new theorems related to all rearrangements
of a given set in Rn , denoted (x) and use the results to prove some new Jensen type inequalities
for convex, superquadratic, strongly convex and 1 -quasiconvex functions.
A note on the best constants in some hardy inequalities
(Journal article; Tidsskriftartikkel; Peer reviewed, 2015)
Abstract. The sharp constants in Hardy type inequalities are known only in a few cases. In this paper we discuss some situations when such sharp constants are known, but also some new sharp constants are derived both in one-dimensional and multi-dimensional cases.