Lars-Erik Persson

Convex functions and their applications : a contemporary approach

This second edition provides a thorough introduction to contemporary convex function theory with many new results. A large variety of subjects are covered, from the one real variable case to some o ...

Weighted inequalities of Hardy type

Hardys Inequality and Related Topics Some Weighted Norm Inequalities The Hardy-Steklov Operator Higher Order Hardy Inequalities Fractional Order Hardy Inequalities Integral Operators on the Cone of Monotone Functions.

The Prehistory of the Hardy Inequality

(2006). The Prehistory of the Hardy Inequality. The American Mathematical Monthly: Vol. 113, No. 8, pp. 715-732.

REITERATED HOMOGENIZATION OF NONLINEAR MONOTONE OPERATORS

In this paper, the authors study reiterated homogenization of nonlinear equations of the form -div(a(x,x/e,x/e2,Due))=f, where a is periodic in the first two arguments and monotone in the third. It is proved that ue converges weakly in W1,p(Ω) (and even in some multiscale sense), as e→0 to the solution u0 of a limit problem. Moreover, an explicit expression for the limit problem is given. The main results were also stated in [15]. This article presents the complete proofs of these results.

Generalized duality of some Banach function spaces

Abstract The set of multipliers from one vector space to another vector space may be seen as a generalized dual space in the sense of Kothe. We give some properties of this kind of duality and prove precise estimates concerning generalized duality of X P -spaces, Lebesgue, Lorentz, Marcinkiewicz and Orlicz spaces. We complement and unify several previous results of this kind.

Weighted Integral Inequalities with the Geometric Mean Operator

The geometric mean operator is defined by Gf(x) = exp(1/x∫0x logf(t)dt). A precise two-sided estimate of the norm ||G|| = supf≠0 ||Gf||Luq/||f||Lvq for 0

Sharp Weighted Multidimensional Integral Inequalities for Monotone Functions

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 dimensio ...

Equivalence of Hardy-type inequalities with general measures on the cones of non-negative respective non-increasing functions

Some Hardy-type integral inequalities in general measure spaces, where the corresponding Hardy operator is replaced by a more general Volterra type integral operator with kernel k(x,y), are considered. The equivalence of such inequalities on the cones of non-negative respective non-increasing functions are established and applied.

On strengthened Hardy and Pólya-Knopp's inequalities

In this paper we prove a strengthened general inequality of the Hardy-Knopp type and also derive its dual inequality. Furthermore, we apply the obtained results to unify the strengthened classical Hardy and Polya-Knopps inequalities deriving them as special cases of the obtained general relations. We discuss Polya-Knopps inequality, compare it with Levin-Cochran-Lees inequalities and point out that these results are mutually equivalent. Finally, we also point out a reversed Polya-Knopp type inequality.

Characterisation of Embeddings in Lorentz Spaces

Characterization of embeddings in Lorentz spaces using a method of discretization and anti-discretization