Four major existential themes are explored, as they relate to the predicament of the relative supporting a demented elderly dependent at home. These issues, namely, death, isolation, freedom, and… (More)

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… (More)

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… (More)

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… (More)

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… (More)

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… (More)

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… (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… (More)

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… (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… (More)