Lars‐Erik Persson
YOU?
Author Swipe
View article: Hardy-Hilbert type inequalities on homogeneous groups-An introduction and generalization to the kernel case
Hardy-Hilbert type inequalities on homogeneous groups-An introduction and generalization to the kernel case Open
There is a lot of information available concerning Hardy-Hilbert type inequalities in one or more dimensions. In this paper we introduce the development of such inequalities on homogeneous groups. Moreover, we point out a unification of se…
View article: Some aspects of web-courses in mathematics based on PC screen recorded video lectures
Some aspects of web-courses in mathematics based on PC screen recorded video lectures Open
In this paper we will describe and discuss two graduate level web-based mathematics courses based on PC screen recorded video lectures. These courses have been developed by the first author of this paper and followed by master’s students a…
View article: Approximation by T means of Walsh–Fourier series in Lebesgue spaces and Lipschitz classes
Approximation by T means of Walsh–Fourier series in Lebesgue spaces and Lipschitz classes Open
In this paper we present and prove some new results concerning the rate of approximation of T means of functions in L^p(G) and in lip (\alpha, p), for 1\leq p <\infty and \alpha > 0. As a corollary, we obtain some new as well as known appr…
View article: Oscillatory and spectral properties of a class of fourth-order differential operators via a new Hardy-type inequality
Oscillatory and spectral properties of a class of fourth-order differential operators via a new Hardy-type inequality Open
In this paper, we study oscillatory properties of a fourth-order differential equation and spectral properties of a corresponding differential operator. These properties are established by f irst proving a new second-order Hardy-type inequ…
View article: Some New Weak $$(H_p-L_p)$$-Type Inequality for Weighted Maximal Operators of Partial Sums of Walsh–Fourier Series
Some New Weak $$(H_p-L_p)$$-Type Inequality for Weighted Maximal Operators of Partial Sums of Walsh–Fourier Series Open
In this paper, we introduce some new weighted maximal operators of the partial sums of the Walsh–Fourier series. We prove that for some “optimal” weights these new operators indeed are bounded from the martingale Hardy space $$H_{p}(G)$$ …
View article: Some new weak $(H_p-L_p)$ type inequality for weighted maximal operators of Walsh-Fourier series
Some new weak $(H_p-L_p)$ type inequality for weighted maximal operators of Walsh-Fourier series Open
In this paper we introduce some new weighted maximal operators of the partial sums of the Walsh-Fourier series. We prove that for some "optimal" weights these new operators indeed are bounded from the martingale Hardy space $H_{p}$ to the …
View article: $(H_p-L_p)$ type inequalities for subsequences of Nörlund means of Walsh-Fourier series
$(H_p-L_p)$ type inequalities for subsequences of Nörlund means of Walsh-Fourier series Open
We investigate the subsequence $\{t_{2^n}f \}$ of Nörlund means with respect to the Walsh system generated by non-increasing and convex sequences. In particular, we prove that a big class of such summability methods are not bounded from th…
View article: Sharpness of some Hardy-type inequalities
Sharpness of some Hardy-type inequalities Open
The current status concerning Hardy-type inequalities with sharp constants is presented and described in a unified convexity way. In particular, it is then natural to replace the Lebesgue measure $dx$ with the Haar measure $dx/x.$ There ar…
View article: Weighted maximal operators of Fejér means of Walsh-Fourier series in the martingale Hardy space $H_{1/2}$
Weighted maximal operators of Fejér means of Walsh-Fourier series in the martingale Hardy space $H_{1/2}$ Open
In this paper we derive the restricted weighted maximal operator, defined by ${\sup }_{k\in \mathbb{N}}\left(\left\vert σ_{k}F\right\vert/A^2_k\right)$ of Fejér means of Walsh-Fourier series and prove that the it is bounded from the martin…
View article: Some new restricted maximal operators of Fejér means of Walsh-Fourier series in the space $H_{1/2}$
Some new restricted maximal operators of Fejér means of Walsh-Fourier series in the space $H_{1/2}$ Open
In this paper we derive the maximal subspace of natural numbers $\left\{n_{k}:k\geq 0\right\}$, such that the restricted maximal operator, defined by $\sup_{k\in \mathbb{N}}\left\vert σ_{n_{k}}F \right\vert$ on this subspace of Fejér means…
View article: On some new weighted maximal operators of Fejér means of Walsh-Fourier series
On some new weighted maximal operators of Fejér means of Walsh-Fourier series Open
In this paper we introduce and investigate a new restricted weighted maximal operator of Fejér means of Walsh-Fourier series and prove that the it is bounded from the martingale Hardy space H 1/2 ( G ) to the Lebesgue space L 1/2 ( G ). Th…
View article: On the Heat and Wave Equations with the Sturm-Liouville Operator in Quantum Calculus
On the Heat and Wave Equations with the Sturm-Liouville Operator in Quantum Calculus Open
In this paper, we explore a generalised solution of the Cauchy problems for the q -heat and q -wave equations which are generated by Jackson’s and the q -Sturm-Liouville operators with respect to t and x , respectively. For this,…
View article: Well-posedness of heat and wave equations generated by Rubin's q-difference operator in Sobolev spaces
Well-posedness of heat and wave equations generated by Rubin's q-difference operator in Sobolev spaces Open
In this paper, we investigate difference-differential operators of parabolic and hyperbolic types. Namely, we consider non-homogenous heat and wave equations for Rubin's difference operator. Well-posedness results are obtained in appropria…
View article: Well-posedness of heat and wave equations generated by Rubin’s q-difference operator in Sobolev spaces
Well-posedness of heat and wave equations generated by Rubin’s q-difference operator in Sobolev spaces Open
In this paper, we investigate difference-differential operators of parabolic and hyperbolic types. Namely, we consider non-homogenous heat and wave equations for Rubin?s difference operator. Wellposedness results are obtained in appropriat…
View article: Some new multidimensional Cochran-Lee and Hardy type inequalities
Some new multidimensional Cochran-Lee and Hardy type inequalities Open
A multidimensional Cochran-Lee operator is introduced and investigated in the frame of Hardy-type inequalities with parameters 0<p⩽q<∞. Moreover, for the case p=q and power weights even the sharp constant is derived, thus generalizing the …
View article: Refinements of Bennett type inequalities
Refinements of Bennett type inequalities Open
In this paper we discuss, complement and improve some Bennett type inequalities. In particular,we prove a new refinement of a Bennett type inequality using super quadracity argument.
View article: Some new refinements of the Young, H older and Minkowski inequalities
Some new refinements of the Young, H older and Minkowski inequalities Open
We prove and discuss some new refined Hölder’s inequalities for any p > 1 and also a reversed version for 0 < p < 1. The key is to use the concept of superquadraticity, strong convexity and to first prove the corresponding refinements of t…
View article: Vilenkin–Lebesgue Points and Almost Everywhere Convergence for Some Classical Summability Methods
Vilenkin–Lebesgue Points and Almost Everywhere Convergence for Some Classical Summability Methods Open
The concept of Vilenkin–Lebesgue points was introduced in [12], where the almost everywhere convergence of Fejer means of Vilenkin–Fourier series was proved. In this paper, we present a different (and simpler) approach to prove a similar r…
View article: Some new resuts concering strong convergence of Fejér means with respect to Vilenkin systems
Some new resuts concering strong convergence of Fejér means with respect to Vilenkin systems Open
UDC 517.5 We prove some new strong convergence theorems for partial sums and Fej\'er means with respect to the Vilenkin system.