| 1. |
- Nikolova, Ludmila, et al.
(författare)
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Some new inequalities involving the Hardy operator
- 2020
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Ingår i: Mathematische Nachrichten. - Weinheim, Germany : Wiley-VCH Verlagsgesellschaft. - 0025-584X .- 1522-2616. ; 293:2, s. 376-385
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we derive some new inequalities involving the Hardy operator, using some estimates of the Jensen functional, continuous form generalization of the Bellman inequality and a Banach space variant of it. Some results are generalized to the case of Banach lattices on 0,?],0<?≤∞.
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| 2. |
- Asekritova, Irina, et al.
(författare)
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Lions-Peetre Reiteration Formulas for Triples and Their Application
- 2001
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Ingår i: Studia Mathematica. - : Institute of Mathematics, Polish Academy of Sciences. - 0039-3223 .- 1730-6337. ; 145:3, s. 219-254
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Tidskriftsartikel (refereegranskat)abstract
- We present, discuss and apply two reiteration theorems for triples of quasi-Banach function lattices. Some interpolation results for block-Lorentz spaces and triples of weighted Lp-spaces are proved. By using these results and a wavelet theory approach we calculate (θ,q)-spaces for triples of smooth function spaces (such as Besov spaces, Sobolev spaces, etc.). In contrast to the case of couples, for which even the scale of Besov spaces is not stable under interpolation, for triples we obtain stability in the frame of Besov spaces based on Lorentz spaces. Moreover, by using the results and ideas of this paper, we can extend the Stein–Weiss interpolation theorem known for Lp(μ)-spaces with change of measures to Lorentz spaces with change of measures. In particular, the results obtained show that for some problems in analysis the three-space real interpolation approach is really more useful than the usual real interpolation between couples.
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| 3. |
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| 4. |
- Asekritova, Irina, et al.
(författare)
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Lizorkin-Freitag Formula for Several Weighted Lp Spaces and Vector-Valued Interpolation
- 2005
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Ingår i: Studia Mathematica. - : Institute of Mathematics, Polish Academy of Sciences. - 0039-3223 .- 1730-6337. ; 170:3, s. 227-239
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Tidskriftsartikel (refereegranskat)abstract
- A complete description of the real interpolation space L=(Lp0(ω0),…,Lpn(ωn))θ⃗ ,q is given. An interesting feature of the result is that the whole measure space (Ω,μ) can be divided into disjoint pieces Ωi (i∈I) such that L is an lq sum of the restrictions of L to Ωi, and L on each Ωi is a result of interpolation of just two weighted Lp spaces. The proof is based on a generalization of some recent results of the first two authors concerning real interpolation of vector-valued spaces.
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| 5. |
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| 6. |
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| 7. |
- Kaijser, Sten, et al.
(författare)
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Hardy-type inequalities via convexity
- 2005
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 8:3, s. 403-417
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Tidskriftsartikel (refereegranskat)abstract
- A recently discovered Hardy-Pólya type inequality described by a convex function is considered and further developed both in weighted and unweighted cases. Also some corresponding multidimensional and reversed inequalities are pointed out. In particular, some new multidimensional Hardy and Pólya-Knopp type inequalities and some new integral inequalities with general integral operators (without additional restrictions on the kernel) are derived
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| 8. |
- Maligranda, Lech, et al.
(författare)
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On n-th James and Khintchine constants of Banach spaces
- 2008
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 11:1, s. 1-22
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Tidskriftsartikel (refereegranskat)abstract
- For any Banach space X the n-th James constants J(n)(X) and the n-th Khintchine constants K-p,q(n)(X) are investigated and discussed. Some new properties of these constants are presented. The main result is an estimate of the n-th Khintchine constants K-p,q(n)(X) by the n-th James constants Jn (X). In the case of n = 2 and p = q = 2 this estimate is even stronger and improvs an earlier estimate proved by Kato-Maligranda-Takahashi
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| 9. |
- Nikolova, Ludmila, et al.
(författare)
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A new look at classical inequalities involving Banach lattice norms
- 2017
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Ingår i: Journal of inequalities and applications. - : Springer. - 1025-5834 .- 1029-242X. ; 2017
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Tidskriftsartikel (refereegranskat)abstract
- Some classical inequalities are known also in a more general form of Banach lattice norms and/or in continuous forms (i.e., for ‘continuous’ many functions are involved instead of finite many as in the classical situation). The main aim of this paper is to initiate a more consequent study of classical inequalities in this more general frame. We already here contribute by discussing some results of this type and also by deriving some new results related to classical Popoviciu’s, Bellman’s and Beckenbach-Dresher’s inequalities.
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| 10. |
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