| 1. |
- Adeleke, E.O., et al.
(författare)
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On a new class of Hardy-type inequalities
- 2012
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Ingår i: Journal of inequalities and applications. - 1025-5834 .- 1029-242X. ; 2012:259
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we generalize a Hardy-type inequality to the class of arbitrary non-negative functions bounded from below and above with a convex function multiplied with positive real constants. This enables us to obtain new generalizations of the classical integral Hardy's, Hardy-Hilbert's, Hardy-Littlewood-P\'{o}lya's and P\'{o}lya-Knopp's inequalities as well as of Godunova's and of some recently obtained inequalities in multidimensional settings. Finally, we apply a similar idea to functions bounded from below and above with a superquadratic function.
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| 2. |
- Barza, Sorina, 1967-, et al.
(författare)
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Some new sharp limit Hardy-type inequalities via convexity
- 2014
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Ingår i: Journal of inequalities and applications. - : Springer. - 1025-5834 .- 1029-242X. ; 2014
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Tidskriftsartikel (refereegranskat)abstract
- Some new limit cases of Hardy-type inequalities are proved, discussed and compared. In particular, some new refinements of Bennett's inequalities are proved. Each of these refined inequalities contain two constants, and both constants are in fact sharp. The technique in the proofs is new and based on some convexity arguments of independent interest.
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| 3. |
- Gogatishvili, Amiran, et al.
(författare)
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Some new iterated Hardy-type inequalities : The case θ=1
- 2013
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Ingår i: Journal of inequalities and applications. - 1025-5834 .- 1029-242X.
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we characterize the validity of the Hardy-type inequality parallel to parallel to integral(infinity)(s)h(z)dz parallel to(p,u,(0,t))parallel to(q,w,(0,infinity)) <= c parallel to h parallel to(1,v,(0,infinity)), where 0 < p < infinity, 0 < q <= +infinity, u, w and v are weight functions on (0, infinity). It is pointed out that this characterization can be used to obtain new characterizations for the boundedness between weighted Lebesgue spaces for Hardy-type operators restricted to the cone of monotone functions and for the generalized Stieltjes operator.
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| 4. |
- Koroleva, Yulia, et al.
(författare)
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On Friedrichs-type inequalities in domains rarely perforated along the boundary
- 2011
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Ingår i: Journal of inequalities and applications. - 1025-5834 .- 1029-242X. ; 2011
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Tidskriftsartikel (refereegranskat)abstract
- This paper is devoted to the Friedrichs inequality, where the domain isperiodically perforated along the boundary. It is assumed that the functionssatisfy homogeneous Neumann boundary conditions on the outer boundary andthat they vanish on the perforation. In particular, it is proved that thebest constant in the inequality converges to the best constant in aFriedrichs-type inequality as the size of the perforation goes to zero muchfaster than the period of perforation. The limit Friedrichs-type inequalityis valid for functions in the Sobolev space $H^{1}$.
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| 5. |
- Kufner, Alois, et al.
(författare)
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Some higher order Hardy inequalities
- 2012
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Ingår i: Journal of inequalities and applications. - 1025-5834 .- 1029-242X.
-
Tidskriftsartikel (refereegranskat)abstract
- We investigate the k-th order Hardy inequality (1-1) for functions satisfying rather general boundary conditions (1-2), show which of these conditions are admissible and derive sufficient, and necessary and sufficient, conditions (for 0 1) on u, v for (1-1) to hold.
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| 6. |
- Nikolova, Ludmila, et al.
(författare)
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The Beckenbach-Dresher inequality in the psi-direct sums of spaces and related results
- 2012
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Ingår i: Journal of inequalities and applications. - 1025-5834 .- 1029-242X. ; 2012:1
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Tidskriftsartikel (refereegranskat)abstract
- Let ~ A : [0; 1] ! R be a concave function with ~ A(0) = ~ A(1) = 1. There is a corresponding map k:k ~ A for which the inverse Minkowski inequality holds. Several properties of that map are obtained. Also, we consider the Beckenbach{Dresher type inequality connected with A-direct sums of Banach spaces and of ordered spaces. In the last section we investigate the properties of functions A!;q and k:k!;q , (0 < ! < 1; q < 1) related to the Lorentz sequence space. Other posibilities for parameters ! and q are considered, the inverse HAolder inequalities and more variants of the Beckenbach{Dresher inequalities are obtained.
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| 7. |
- Persson, Lars-Erik, et al.
(författare)
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What should have happened if Hardy had discovered this?
- 2012
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Ingår i: Journal of inequalities and applications. - 1025-5834 .- 1029-242X. ; 2012:2
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Tidskriftsartikel (refereegranskat)abstract
- First we present and discuss an important proof of Hardy's inequality via Jensen's inequality which Hardy and his collaborators did not discover during the 10 years of research until Hardy finally proved his famous inequality in 1925. If Hardy had discovered this proof, it obviously would have changed this prehistory, and in this article the authors argue that this discovery would probably also have changed the dramatic development of Hardy type inequalities in an essential way. In particular, in this article some results concerning powerweight cases in the finite interval case are proved and discussed in this historical perspective. Moreover, a new Hardy type inequality for piecewise constant p = p(x) is proved with this technique, limiting cases are pointed out and put into this frame.
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| 8. |
- Abramovich, Shoshana, et al.
(författare)
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Some new estimates of the ‘Jensen gap’
- 2016
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Ingår i: Journal of inequalities and applications. - : Springer Science and Business Media LLC. - 1025-5834 .- 1029-242X. ; 2016
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Tidskriftsartikel (refereegranskat)abstract
- Let (μ,Ω) be a probability measure space. We consider the so-called ‘Jensen gap’ J(φ,μ,f)=∫ Ω φ(f(s))dμ(s)−φ(∫ Ω f(s)dμ(s)) for some classes of functions φ. Several new estimates and equalities are derived and compared with other results of this type. Especially the case when φ has a Taylor expansion is treated and the corresponding discrete results are pointed out.
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| 9. |
- Abylayeva, Akbota M., et al.
(författare)
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Boundedness and compactness of a class of Hardy type operators
- 2016
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Ingår i: Journal of inequalities and applications. - : Springer Science and Business Media LLC. - 1025-5834 .- 1029-242X. ; :1
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 10. |
- Akishev, G., et al.
(författare)
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Some new Fourier inequalities for unbounded orthogonal systems in Lorentz–Zygmund spaces
- 2020
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Ingår i: Journal of inequalities and applications. - : Springer. - 1025-5834 .- 1029-242X. ; , s. 1-12
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Tidskriftsartikel (refereegranskat)abstract
- 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 thecase of the Lorentz–Zygmund function spaces Lq,r(log L)α involved and in the casewith an unbounded orthonormal system. More exactly, in this paper we prove anddiscuss some new Fourier inequalities of this type for the limit case L2,r(log L)α, whichcould not be proved with the techniques used in the paper (J. Inequal. Appl.2019:171, 2019).
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