EuDML | Browse

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

Henri Heinich (1990)

Annales de l'I.H.P. Probabilités et statistiques

Medians, continuity, and vanishing oscillation

Jonathan Poelhuis, Alberto Torchinsky (2012)

Studia Mathematica

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.

Mesures de Carleson d’ordre $α$ et solutions au bord de l’équation $\bar{\partial}$

Eric Amar, Aline Bonami (1979)

Bulletin de la Société Mathématique de France

Metric projections and best approximants in Bochner-Orlicz spaces.

Ryszard Pluciennik, Yuwen Wang (1994)

Revista Matemática de la Universidad Complutense de Madrid

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.

Minimal Projections in Tensor-Product Spaces.

W.A. Light (1986)

Mathematische Zeitschrift

Minimal rearrangements of Sobolev functions.

John E. Brothers, William P. Ziemer (1988)

Journal für die reine und angewandte Mathematik

Minimal rearrangements of Sobolev functions

John E. Brothers, William P. Ziemer (1987)

Acta Universitatis Carolinae. Mathematica et Physica

Mixed norms and Sobolev type inequalities

V. I. Kolyada (2006)

Banach Center Publications

We study mixed norm spaces that arise in connection with embeddings of Sobolev and Besov spaces. We prove Sobolev type inequalities in terms of these mixed norms. Applying these results, we obtain optimal constants in embedding theorems for anisotropic Besov spaces. This gives an extension of the estimate proved by Bourgain, Brezis and Mironescu for isotropic Besov spaces.

Modular inequalities for the Hardy averaging operator

Hans P. Heinig (1999)

Mathematica Bohemica

If $P$ is the Hardy averaging operator - or some of its generalizations, then weighted modular inequalities of the form u (Pf) Cv (f) are established for a general class of functions $φ$ . Modular inequalities for the two- and higher dimensional Hardy averaging operator are also given.

Modular spaces over a field with valuation generated by a (ω,ϑ)-convex modular

Ryszard Urbański (1983)

Studia Mathematica

Modulus of continuity of a set function and some of its applications

Wanda Matuszewska, Władysław Orlicz (1975)

Annales Polonici Mathematici

Modulus of dentability in $L ¹ + L^{\infty}$

Adam Bohonos, Ryszard Płuciennik (2008)

Banach Center Publications

We introduce the notion of the modulus of dentability defined for any point of the unit sphere S(X) of a Banach space X. We calculate effectively this modulus for denting points of the unit ball of the classical interpolation space $L ¹ + L^{\infty} .$ Moreover, a criterion for denting points of the unit ball in this space is given. We also show that none of denting points of the unit ball of $L ¹ + L^{\infty}$ is a LUR-point. Consequently, the set of LUR-points of the unit ball of $L ¹ + L^{\infty}$ is empty.

Moments of Measures on Banach Spaces.

Werner Linde (1981)

Mathematische Annalen

Monotone coefficients and monotonicity of Orlicz spaces.

Yanming Lü, Junming Wang, Tingfu Wang (1999)

Revista Matemática Complutense

The criteria for uniform monotonicity, locally uniformly monotonicity and monotonicity of of Orlicz spaces with Luxemburg and Orlicz norms are given. The monotone coefficients of a point and of the spaces are computed.

Monotone substochastic operators and a new Calderón couple

Karol Leśnik (2015)

Studia Mathematica

An important result on submajorization, which goes back to Hardy, Littlewood and Pólya, states that b ⪯ a if and only if there is a doubly stochastic matrix A such that b = Aa. We prove that under monotonicity assumptions on the vectors a and b the matrix A may be chosen monotone. This result is then applied to show that $(\tilde{L^{p}}, L^{\infty})$ is a Calderón couple for 1 ≤ p < ∞, where $\tilde{L^{p}}$ is the Köthe dual of the Cesàro space $C e s_{p^{'}}$ (or equivalently the down space $L_{↓}^{p^{'}}$ ). In particular, $(\tilde{L ¹}, L^{\infty})$ is a Calderón couple, which gives a...

Currently displaying 581 – 600 of 1406

Previous Page 30 Next