| 1. |
- Asekritova, Irina, et al.
(author)
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Lions-Peetre Reiteration Formulas for Triples and Their Application
- 2001
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In: Studia Mathematica. - : Institute of Mathematics, Polish Academy of Sciences. - 0039-3223 .- 1730-6337. ; 145:3, s. 219-254
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Journal article (peer-reviewed)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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| 2. |
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| 3. |
- Asekritova, Irina, et al.
(author)
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Lizorkin-Freitag Formula for Several Weighted Lp Spaces and Vector-Valued Interpolation
- 2005
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In: Studia Mathematica. - : Institute of Mathematics, Polish Academy of Sciences. - 0039-3223 .- 1730-6337. ; 170:3, s. 227-239
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Journal article (peer-reviewed)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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| 4. |
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| 5. |
- Barza, Sorina, Associate professor, 1967-, et al.
(author)
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Carleson- and Hardy type inequalities in some Banach function spaces
- 2019
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In: Nonlinear Studies. - 1359-8678. ; 26:4, s. 755-766
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Journal article (peer-reviewed)abstract
- Some new inequalities of Carleson- and Hardy- type in Banach function space settings are proved and discussed. In particular, these theorems both generalize and unify several classical inequalities e.g. those by Hardy, Polya-Knopp, Carleman, Hardy-Knopp and Carleson. As applications some new inequalities are pointed out.
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| 6. |
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| 7. |
- Kaijser, Sten, et al.
(author)
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Hardy-type inequalities via convexity
- 2005
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In: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 8:3, s. 403-417
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Journal article (peer-reviewed)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.
(author)
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On n-th James and Khintchine constants of Banach spaces
- 2008
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In: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 11:1, s. 1-22
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Journal article (peer-reviewed)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.
(author)
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A new look at classical inequalities involving Banach lattice norms
- 2017
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In: Journal of inequalities and applications. - : Springer. - 1025-5834 .- 1029-242X. ; 2017
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Journal article (peer-reviewed)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. |
- Nikolova, Ludmila, et al.
(author)
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Continuous refinements of some Jensen-type inequalities via strong convexity with applications
- 2022
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In: Journal of inequalities and applications. - : Springer. - 1025-5834 .- 1029-242X. ; 2022:1
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Journal article (peer-reviewed)abstract
- In this paper we prove new continuous refinements of some Jensen type inequalities in both direct and reversed forms. As applications we also derive some continuous refinements of Hermite-Hadamard, Holder, and Popoviciu type inequalities. As particular cases we point out the corresponding results for sums and integrals showing that our results contain both several well-known but also some new results for these special cases.
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| 11. |
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| 12. |
- Nikolova, Ludmila, et al.
(author)
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On interpolation between Xp -spaces
- 1989
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In: Function spaces, differential operators and nonlinear analysis. - Harlow : John Wiley & Sons. - 0470213515 ; , s. 89-107
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Conference paper (peer-reviewed)
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| 13. |
- Nikolova, Ludmila, et al.
(author)
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Refinements of some classical inequalities via superquadraticity
- 2022
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In: Journal of inequalities and applications. - : Springer. - 1025-5834 .- 1029-242X. ; 2022:1
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Journal article (peer-reviewed)abstract
- Some new refined versions of the Jensen, Minkowski, and Hardy inequalities are stated and proved. In particular, these results both generalize and unify several results of this type. Some results are also new for the classical situation.
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| 14. |
- Nikolova, Ludmila, et al.
(author)
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Some new inequalities involving the Hardy operator
- 2020
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In: Mathematische Nachrichten. - Weinheim, Germany : Wiley-VCH Verlagsgesellschaft. - 0025-584X .- 1522-2616. ; 293:2, s. 376-385
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Journal article (peer-reviewed)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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| 15. |
- Nikolova, Ludmila, et al.
(author)
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Some new refinements of the Young, Hölder, and Minkowski inequalities
- 2023
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In: Journal of inequalities and applications. - : Springer. - 1025-5834 .- 1029-242X. ; 2023:1
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Journal article (peer-reviewed)abstract
- We prove and discuss some new refined Hölder inequalities for any p> 1 and also a reversed version for 0 < p< 1. The key is to use the concepts of superquadraticity, strong convexity, and to first prove the corresponding refinements of the Young and reversed Young inequalities. Refinements of the Minkowski and reversed Minkowski inequalities are also given.
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| 16. |
- Nikolova, Ludmila, et al.
(author)
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The Beckenbach-Dresher inequality in the psi-direct sums of spaces and related results
- 2012
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In: Journal of inequalities and applications. - 1025-5834 .- 1029-242X. ; 2012:1
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Journal article (peer-reviewed)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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| 17. |
- Nikolova, Ludmila, et al.
(author)
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Weighted Hardy and Pólya-Knopp inequalities with variable limits
- 2007
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In: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 10:3, s. 547-557
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Journal article (peer-reviewed)abstract
- A new scale of characterizations for the weighted Hardy inequality with variable limits is proved for the case 1 < p ≤ q < ∞. A corresponding scale of characterizations for the (limit) weighted Pólya-Knopp inequality is also derived and discussed.
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| 18. |
- Nikolova, Ludmila Y., et al.
(author)
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A study of some constants for Banach spaces
- 2004
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In: Proceedings of the Bulgarian Academy of Sciences. - 0861-1459. ; 57:2, s. 5-8
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Journal article (peer-reviewed)abstract
- The authors of the short communication under consideration recall the definitions of the James nonsquare constant $ J(X) $, the Jordan-von Neumann constant $ C_{NJ}(X) $, the generalized James constant $ \beta_{n}(X) $ and the constant $ T_{p(s)}^{(n)}(X) $ of a Banach space $ X $. Many inequalities among these constants are proposed in two theorems, 8 corollaries and several propositions. The proofs of these results can be found in a Research report of Lulea Univ., 2003.
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| 19. |
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| 20. |
- Nikolova, Ludmila Y., et al.
(author)
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On Clarkson's inequality, type and cotype for the Edmunds-Triebel logarithmic spaces
- 2003
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In: Archiv der Mathematik. - : Springer Science and Business Media LLC. - 0003-889X .- 1420-8938. ; 80:2, s. 165-176
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Journal article (peer-reviewed)abstract
- We show that the (p, p') Clarkson's inequality holds in the Edmunds-Triebel logarithmic spaces Aq(logA)b,q and in the Zygmund spaces Lp(logL)b(W), for b Î \mathbbR and for suitable 1 £ p £ 2. As a consequence of these results we also obtain some new information about the types and the cotypes of these spaces.
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| 21. |
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