| 1. |
- 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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| 2. |
- Barza, Sorina, et al.
(författare)
-
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, 1967-, et al.
(författare)
-
Sharp weighted multidimensional integral inequalities for monotone functions
- 2000
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Ingår i: Mathematische Nachrichten. - : John Wiley & Sons. - 0025-584X .- 1522-2616. ; 210:1, s. 43-58
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Tidskriftsartikel (refereegranskat)abstract
- We prove sharp weighted inequalities for general integral operators acting on monotone functions of several variables. We extend previous results in one dimension, and also those in higher dimension for particular choices of the weights (power weights, etc.). We introduce a new kind of conditions, which take into account the more complicated structure of monotone functions in dimension n > 1, and give an example that shows how intervals are not enough to characterize the boundedness of the operators (contrary to what happens for n = 1). We also give several applications of our techniques.
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| 4. |
- Barza, Sorina, 1967-, et al.
(författare)
-
Sharp weighted multidimensional integral inequalities of Chebyshev type
- 1999
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Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 236:2, s. 243-253
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Tidskriftsartikel (refereegranskat)abstract
- We prove a general Chebyshev inequality for monotone functions in higher dimensions. This result generalizes the classical one-dimensional inequality and recovers some extensions already known for product weights. In all cases we find the best constant in the inequality. We also consider the case of more general operators.
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