Means of vector-valued functions and projections which commute with the action of a group
Measurability and Pettis integration in Hilbert spaces.
Measurability of linear operators in the Skorokhod topology.
Measurable bundles of -algebras.
Measurable functionals on function spaces
We prove that all measurable functionals on certain function spaces are measures; this improves the (known) results about weak sequential completeness of spaces of measures. As an application, we prove several results of this form: if the space of invariant functionals on a function space is separable then every invariant functional is a measure.
Measurable multifunctions and their applications to convex integral functionals.
Measure concentration for compound Poisson distributions.
Measure density and extendability of Sobolev functions.
Measure of noncompactness of subsets of Lebesgue spaces
Measures of non-compactness in Orlicz modular spaces.
In this paper we show that the ball-measure of non-compactness of a norm bounded subset of an Orlicz modular space L-Psi is equal to the limit of its n-widths. We also obtain several inequalities between the measures of non-compactness and the limit of the n-widths for modular bounded subsets of L-Psi which do not have Delta-2-condition. Minimum conditions on Psi to have such results are specified and an example of such a function Psi is provided.
Médianes vectorielles
Medians, continuity, and vanishing oscillation
We consider properties of medians as they pertain to the continuity and vanishing oscillation of a function. Our approach is based on the observation that medians are related to local sharp maximal functions restricted to a cube of ℝⁿ.
Meilleures constantes et inégalités de Sobolev optimales sur les variétés riemanniennes compactes
Mergelyan type theorems for some function spaces.
Mesures de Carleson d’ordre et solutions au bord de l’équation
Méthodes de réalisation de produit scalaire et de problème de moments avec maximisation d'entropie
We develop several methods of realization of scalar product and generalized moment problems. Constructions are made by use of a Hilbertian method or a fixed point method. The constructed solutions are rational fractions and exponentials of polynomials. They are connected to entropy maximization. We give the general form of the maximizing solution. We show how it is deduced from the maximizing solution of the algebraic moment problem.
Metric projections and best approximants in Bochner-Orlicz spaces.
In the first section of this paper there are given criteria for strict convexity and smoothness of the Bochner-Orlicz space with the Orlicz norm as well as the Luxemburg norm. In the second one that geometrical properties are applied to the characterization of metric projections and zero mean valued best approximants to Bochner-Orlicz spaces.
Metric Sobolev spaces
We describe an approach to establish a theory of metric Sobolev spaces based on Lipschitz functions and their pointwise Lipschitz constants and the Poincaré inequality.
Minimal Projections in Tensor-Product Spaces.
Minimal rearrangements of Sobolev functions.