Showing papers on "Birnbaum–Orlicz space published in 1983"
Book•
01 Jan 1983
TL;DR: In this article, the authors measure smoothness using Atoms and Pointwise Multipliers, Wavelets, Spaces on Lipschitz Domains, Wavelet and Sampling Numbers.
Abstract: How to Measure Smoothness.- Atoms and Pointwise Multipliers.- Wavelets.- Spaces on Lipschitz Domains, Wavelets and Sampling Numbers.- Anisotropic Function Spaces.- Weighted Function Spaces.- Fractal Analysis: Measures, Characteristics, Operators.- Function Spaces on Quasi-metric Spaces.- Function Spaces on Sets.
4,099 citations
Book•
01 Nov 1983
TL;DR: In this paper, a family of modulars depending on a parameter is described, and some applications of modular spaces are discussed, including orlicz spaces and countably modulared spaces.
Abstract: Modular spaces.- Orlicz spaces.- Countably modulared spaces.- Families of modulars depending on a parameter.- Some applications of modular spaces.
1,732 citations
TL;DR: In this paper, the authors present a survey of the properties of multipliers in the spaces of Sobolev spaces and Bessel potentials and show that multipliers can be used to obtain a measure of functions from the spaces.
Abstract: CONTENTS Introduction Chapter I. Embedding theorems for Sobolev spaces § 1.1. The summability with respect to a measure of functions from the spaces and , § 1.2. The summability with respect to a measure of functions from the spaces and Chapter II. Multipliers in pairs of Sobolev spaces § 2.1. A description of the spaces and § 2.2. The space § 2.3. The space Chapter III. A survey of other results about spaces of multipliers § 3.1. Multipliers in pairs of spaces of Bessel potentials § 3.2. Multipliers in pairs of Slobodetskii spaces § 3.3. Some properties of multipliers § 3.4. Multipliers in pairs of Sobolev spaces in a domain § 3.5. Multipliers on the space BMO § 3.6. Multipliers on certain spaces of analytic functions § 3.7. Applications of multipliers References
242 citations
66 citations
Journal Article•
TL;DR: In this paper, the authors implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.php).
Abstract: L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
59 citations
TL;DR: In this article, the authors obtained new bounds for the error in polynomial approximation in Sobolev spaces in an open bounded set which is star-shaped with respect to every point in a set of positive measure $B \subset \Omega $.
Abstract: We obtain new bounds for the error in the polynomial approximation in Sobolev spaces in an open bounded set which is star-shaped with respect to every point in a set of positive measure $B \subset \Omega $. This estimate follows by applying the Hardy–Littlewood maximal function.
43 citations
01 Jan 1983
TL;DR: In this paper, three Hankel invariant test function spaces and associated generalized function spaces are introduced, and the elements of the respective test functions are described both in functional analytic and in classical analytic terms.
Abstract: Three Hankel invariant test function spaces and the associated generalized function spaces are introduced. The elements of the respective test function spaces are described both in functional analytic and in classical analytic terms. It is shown that one of the test function spaces equals the space Hμ of Zemanian.
30 citations
18 citations
TL;DR: In this article, the linear representations of the finite cotriangular space (copolar spaces of order 2) in vector spaces over GF(2) were classified into quadratic and symplectic forms.
01 Feb 1983
TL;DR: In this article, the Fourier method was used for complex interpolation of martingale HP spaces and Sobolev spaces, and the result was proved for all the spaces.
Abstract: Using Fourier type arguments we provide a very simple proof of recent results on complex interpolation of HP spaces and martingale HP spaces. The same method gives a new result on complex interpolation of Sobolev spaces. In a recent article (cf. [4]) S. Janson and P. Jones obtained a description of the complex method of interpolation for HP spaces and martingale HP spaces. Some of their main results are summarized in the following (for definiteness all our spaces (except the martingale spaces) are based on Rn). THEOREM A. (i) Let XO be either H1 or L' and let Xl be either L? or BMO; then (Xo, X,)@ = LP9, 0 < 0 < 1, I/Po = 0. (ii) Let XO be either MH1 or ML' and let Xl be either ML' or MBMO; then (Xo, X,)@ = MLP9, 0 < 0 < 1, I/Po = 0. The purpose of this paper is to provide a very simple proof of this theorem. Moreover, the method we use also yields the following interpolation theorem for Sobolev spaces.
TL;DR: In this article, the authors review several properties of some constants considered in the study of the geometry of Banach spaces and relate many results on them published recently, partly also on chinese journals.
Abstract: We review several properties of some constants considered in the study of the geometry of Banach spaces. We relate many results on them published recently, partly also on chinese journals.
TL;DR: In this article, the equivalence between the Campanato spaces and homogeneous Lipschitz spaces is shown through the use of elementary and constructive means, which can be defined in terms of derivatives as well as differences.
Abstract: In this paper the equivalence between the Campanato spaces and homogeneous Lipschitz spaces is shown through the use of elementary and constructive means. These Lipschitz spaces can be defined in terms of derivatives as well as differences.
TL;DR: RefReflexive BANCH spaces and separable duals of BANACH spaces posses the RADON-NIKODYM Property as discussed by the authors, and the purpose of this paper is to extend these results to locally convex spaces.
Abstract: Reflexive BANCH spaces and separable duals of BANACH spaces posses the RADON-NIKODYM Property. The purpose of this paper is to extend these results to locally convex spaces. As the examples will show, these RNP-spaces include most spaces which occur frequently in Functional Analysis.
TL;DR: In this article, the existence of an optimal control in Banach spaces for a system characterized by Hammerstein operator equations is proved, and the optimal control is shown to be optimal.
Abstract: We prove the existence of an optimal control in Banach spaces for a system characterized by Hammerstein operator equations.
01 Jan 1983
01 Nov 1983
TL;DR: A new approach to semantics, based on ordered Banach spaces, is proposed, which arises as a generalization of the four particular cases: the Giles' approach to belief structures, its generalization to the non-Boolean case, and “fuzzy extensions” of Boolean as well as of non- Boolean semantics.
Abstract: A new approach to semantics, based on ordered Banach spaces, is proposed. The Banach spaces semantics arises as a generalization of the four particular cases: the Giles' approach to belief structures, its generalization to the non-Boolean case, and “fuzzy extensions” of Boolean as well as of non-Boolean semantics.
01 Jan 1983
TL;DR: In this article, the authors discuss some open problems arising in the uniform and Lipschitz classification of Banach spaces and give the origin or motivation for these problems, as well as a brief survey.
Abstract: In this brief survey we want to discuss some open problems arising in the uniform and Lipschitz classification of Banach spaces. We shall mention some (recent) results which are the origin or give the motivation for these problems. The fundamental problem, which created the development of the field, is the following: Are any two uniformly homeomorphic (resp. Lipschitz homeomorphic) Banach spaces isomorphic? Throughout this paper isomorphic means linearly isomorphic. Recall also that two Banach spaces X and Y are uniformly homeomorphic if there is a one-to-one mapping f from X onto Y such that f and f-1 are uniformly continuous. X and Y are called Lipschitz homeomorphic if f is one-to-one and satisfies