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- 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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| 2. |
- 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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| 3. |
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| 4. |
- 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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| 5. |
- 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)
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| 6. |
- 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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| 7. |
- 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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| 8. |
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| 9. |
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| 10. |
- Barza, Sorina, et al.
(författare)
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Mixed norm and multidimensional Lorentz spaces
- 2006
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Ingår i: Positivity (Dordrecht). - : Springer Science and Business Media LLC. - 1385-1292 .- 1572-9281. ; 10:3, s. 539-554
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Tidskriftsartikel (refereegranskat)abstract
- In the last decade, the problem of characterizing the normability of the weighted Lorentz spaces has been completely solved ([16], [7]). However, the question for multidimensional Lorentz spaces is still open. In this paper, we consider weights of product type, and give necessary and sufficient conditions for the Lorentz spaces, defined with respect to the two-dimensional decreasing rearrangement, to be normable. To this end, it is also useful to study the mixed norm Lorentz spaces. Finally, we prove embeddings between all the classical, multidimensional, and mixed norm Lorentz spaces.
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