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- Sorina Barza, Javier Soria
- 2008

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. Mathematics Subject Classification 2000: 46E30, 46B25.

- Sorina Barza, Alois Kufner
- 2002

Let + := {(x1, . . . , xN ) ; xi 0, i = 1, 2, . . . , N} and + := + . Assume that f : + → + is monotone which means that it is monotone with respect to each variable. We denote f ↓, when f is decreasing (= nonincreasing) and f ↑ when f is increasing (= nondecreasing). Throughout this paper ω, u, v are positive measurable functions defined on + , N 1. A… (More)

- Sorina Bârză, Emil C. Popa
- 2005

We give upper and lower bounds estimates for the best constant which appears in a multidimensional integral inequality, in the particular case of homogeneous weights. 2000 Mathematics Subject Classification: 26D15, 26B99

Recommended by Wing-Sum Cheung 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.

We give a generalization of a one-dimensional Carlson type inequality due to G.S. Yang and J.-C. Fang and a generalization of a multidimensional type inequality due to L. Larsson. We point out the strong and weak parts of each result.

The theory of weighted inequalities for the Hardy operator, acting on monotone functions in R+, was first introduced in [2]. Extensions of these results to higher dimensions have been considered only in very specific cases: in particular, in the diagonal case, for p = 1 only (see [3]). The main difficulty in this context is that the level sets of the… (More)

Let f be a non-negative function on R, which is radially monotone (0 < f ↓ r). For 1 < p < ∞, g ≥ 0 and v a weight function, an equivalent expression for sup f↓r ∫ Rn fg (∫ Rn f pv ) 1 p is proved as a generalization of the usual Sawyer duality principle. Some applications involving boundedness of certain integral operators are also given.

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… (More)

The study of the normability of the Lorentz spaces L(R, μ) goes back to the work of G.G. Lorentz [10, 11] (see also [13, 3, 2] for a more recent account of the normability results for the weighted Lorentz spaces). The condition defining these spaces is given in terms of the distribution function and, equivalently, the non-increasing rearrangement of f (see… (More)

- S Barza
- Canadian journal of psychiatry. Revue canadienne…
- 1985