| 1. |
- Barza, Sorina, 1967-, et al.
(författare)
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Best constants between equivalent norms in Lorentz sequence spaces
- 2012
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Ingår i: Journal of Function Spaces and Applications. - : Hindawi Limited. - 0972-6802 .- 1758-4965. ; 2012
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Tidskriftsartikel (refereegranskat)abstract
- We find the best constants in inequalities relating the standard norm, the dual norm, and the norm ‖ 푥 ‖ ( 푝 , 푠 ) ∑ ∶ = i n f { 푘 ‖ 푥 ( 푘 ) ‖ 푝 , 푠 } , where the infimum is taken over all finite representations ∑ 푥 = 푘 푥 ( 푘 ) in the classical Lorentz sequence spaces. A crucial point in this analysis is the concept of level sequence, which we introduce and discuss. As an application, we derive the best constant in the triangle inequality for such spaces.
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| 2. |
- Barza, Sorina, et al.
(författare)
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Multidimensional rearrangement and Lorentz spaces
- 2004
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Ingår i: Acta Mathematica Hungarica. - 0236-5294 .- 1588-2632. ; 104:3, s. 203-224
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Tidskriftsartikel (refereegranskat)abstract
- We define a multidimensional rearrangement, which is related to classical inequalities for functions that are monotone in each variable. We prove the main measure theoretical results of the new theory and characterize the functional properties of the associated weighted Lorentz spaces.
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| 3. |
- Barza, Sorina, et al.
(författare)
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Some multiplicative inequalities for inner products and of the Carlson type
- 2008
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Ingår i: Journal of inequalities and applications. - : Springer Science and Business Media LLC. - 1025-5834 .- 1029-242X.
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Tidskriftsartikel (refereegranskat)abstract
- We prove a multiplicative inequality for inner products, which enables us to deduce improvements of inequalities of the Carlson type for complex functions and sequences, and also other known inequalities.
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| 4. |
- 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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| 5. |
- Barza, Sorina, et al.
(författare)
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A matriceal analogue of Fejer's theory
- 2003
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Ingår i: Mathematische Nachrichten. - : Wiley. - 0025-584X .- 1522-2616. ; 260:1, s. 14-20
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Tidskriftsartikel (refereegranskat)abstract
- J. Arazy [1] pointed out that there is a similarity between functions defined on the torus and infinite matrices. In this paper we discuss and develop in the framework of matrices Fejer's theory for Fourier series.
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| 6. |
- Barza, Sorina, 1967-, et al.
(författare)
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A new variational characterization of Sobolev spaces
- 2015
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Ingår i: Journal of Geometric Analysis. - : Springer Science and Business Media LLC. - 1050-6926 .- 1559-002X. ; 25:4, s. 2185-2195
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Tidskriftsartikel (refereegranskat)abstract
- We obtain a new variational characterization of the Sobolev space $W_p^1(\Omega)$ (where $\Omega\subseteq\R^n$ and $p>n$). This is a generalization of a classical result of F. Riesz. We also consider some related results.
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| 7. |
- Barza, Sorina, et al.
(författare)
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A Sawyer duality principle for radially monotone functions in Rn
- 2005
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Ingår i: Journal of Inequalities in Pure and Applied Mathematics. - 1443-5756. ; 6:2
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Tidskriftsartikel (refereegranskat)abstract
- Let f be a non-negative function on ℝn, which is radially monotone (0 < f↓ r). For 1 < p < ∞, g ≥ 0 and v a weight function, an equivalent expression for sup ∫ℝ fg/f↓r(∫ℝn fp v)1/p is proved as a generalization of the usual Sawyer duality principle. Some applications involving boundedness of certain integral operators are also given. © 2005 Victoria University
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| 8. |
- Barza, Sorina, et al.
(författare)
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Carlson type inequalities
- 1998
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Ingår i: Journal of inequalities and applications. - 1025-5834 .- 1029-242X. ; 2:2, s. 121-135
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Tidskriftsartikel (refereegranskat)abstract
- A scale of Carlson type inequalities are proved and the best constants are found. Some multidimensional versions of these inequalities are also proved and it is pointed out that also a well-known inequality by Beurling-Kjellberg is included as an endpoint case.
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| 9. |
- Barza, Sorina, et al.
(författare)
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Duality theorem over the cone of monotone functions and sequences in higher dimensions
- 2002
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Ingår i: Journal of inequalities and applications. - 1025-5834 .- 1029-242X. ; 7:1, s. 79-108
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Tidskriftsartikel (refereegranskat)abstract
- Let f be a non-negative function defined on ℝ+n which is monotone in each variable separately. If 1 < p < ∞, g ≥ 0 and v a product weight function, then equivalent expressions for sup ∫ℝ(+)(n) fg/(ℝ+nfpv)1/p are given, where the supremum is taken over all such functions f. Variants of such duality results involving sequences are also given. Applications involving weight characterizations for which operators defined on such functions (sequences) are bounded in weighted Lebesgue (sequence) spaces are also pointed out.
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| 10. |
- Barza, Sorina, Associate professor, 1967-, et al.
(författare)
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End-point norm estimates for Cesaro and Copson operators
- 2024
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Ingår i: Annali di Matematica Pura ed Applicata. - : Springer. - 0373-3114 .- 1618-1891. ; 203, s. 989-1013
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Tidskriftsartikel (refereegranskat)abstract
- For a large class of operators acting between weighted l(infinity) spaces, exact formulas are given for their norms and the norms of their restrictions to the cones of nonnegative sequences; nonnegative, nonincreasing sequences; and nonnegative, nondecreasing sequences. The weights involved are arbitrary nonnegative sequences and may differ in the domain and codomain spaces. The results are applied to the Cesaro and Copson operators, giving their norms and their distances to the identity operator on the whole space and on the cones. Simplifications of these formulas are derived in the case of these operators acting on power-weighted l(infinity). As an application, best constants are given for inequalities relating the weighted l(infinity) norms of the Cesaro and Copson operators both for general weights and for power weights.
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