Showing papers on "Birnbaum–Orlicz space published in 1995"
Book•
30 Jun 1995
TL;DR: In this paper, Wogen's Theorem Spectral Properties Spectral properties of Compact Composition Operators Spectra: Boundary Fixed Point, Boundary fixed point, boundary fixed point.
Abstract: Introduction Analysis Background A Menagerie of Spaces Some Theorems on Integration Geometric Function Theory in the Disk Iteration of Functions in the Disk The Automorphisms of the Ball Julia-Caratheodory Theory in the Ball Norms Boundedness in Classical Spaces on the Disk Compactness and Essential Norms in Classical Spaces on the Disk Hilbert-Schmidt Operators Composition Operators with Closed Range Boundedness on Hp (BN) Small Spaces Compactness on Small Spaces Boundedness on Small Spaces Large Spaces Boundedness on Large Spaces Compactness on Large Spaces Hilbert-Schmidt Operators Special Results for Several Variables Compactness Revisited Wogen's Theorem Spectral Properties Introduction Invertible Operators on the Classical Spaces on the Disk Invertible Operators on the Classical Spaces on the Ball Spectra of Compact Composition Operators Spectra: Boundary Fixed Point, j'(a)
1,416 citations
Book•
17 Nov 1995
TL;DR: In this paper, the interplay between function space theory and potential theory is discussed. And a surprisingly large part of classical potential theory has been extended to this nonlinear setting, sometimes surprising, usually they are nontrivial and have required new methods.
Abstract: The subject of this book is the interplay between function space theory and potential theory. A crucial step in classical potential theory is the identification of the potential energy of a charge with the square of a Hilbert space norm. This leads to the Dirichlet space of locally integrable functions whose gradients are square integrable. More recently, a generalized potential theory has been developed, which has an analogous relationship to the standard Banach function spaces, Sobolev spaces, Besov spaces etc., that appear naturally in the study of partial differential equations. A surprisingly large part of classical potential theory has been extended to this nonlinear setting. The extensions are sometimes surprising, usually they are nontrivial and have required new methods.
1,370 citations
Book•
01 Jun 1995
TL;DR: In this paper, the authors consider closed sets capacity systems of differential equations with injective symbol and give coarse results on approximation by solutions of a system with surjective symbol approximation in spaces of smooth functions approximation, spaces of Holder functions approximation and spaces of Sobolev functions.
Abstract: Function spaces pseudodifferential operators in the spaces of distributions on closed sets capacity systems of differential equations with injective (surjective) symbol coarse results on approximation by solutions of a system with surjective symbol approximation in spaces of smooth functions approximation in spaces of Holder functions approximation in spaces of Sobolev functions generalized boundary values of solutions of a system with injective symbol. (Part contents).
146 citations
01 Jan 1995
TL;DR: In this paper, local embeddings of Sobolev and Morrey type for Dirichlet forms on spaces of homogeneous type were proved for some general classes of self-adjoint subelliptic operators.
Abstract: — We prove local embeddings of Sobolev and Morrey type for Dirichlet forms on spaces of homogeneous type. Our results apply to some general classes of selfadjoint subelliptic operators as well as to Dirichlet operators on certain self-similar fractals, like the Sierpinski gasket. We also define intrinsic BV spaces and perimeters and prove related isoperimetric inequalities.
63 citations
01 Jan 1995
TL;DR: In this paper, the authors discuss dimensional linear spaces and highlight planar spaces, benz planes, embeddings, coordinatizations, and automorphisms among others, and describe the characterization and embeddability problems for DLS.
Abstract: Publisher Summary
This chapter discusses dimensional linear spaces and highlights planar spaces, benz planes, embeddings, coordinatizations, and automorphisms among others. Dimensional linear spaces (DLS's) are a rather straightforward generalization of the basic structure of elementary geometry. It describes the characterization and embeddability problems for DLS, that is characterize classical DLS's in terms of local or global, combinatorial, geometrical or group-theoretical conditions and find sufficient conditions for DLS's to be embeddable (or coordinatizable, or representable) into projective spaces (or into algebraic spaces). A dimensional linear space (DLS) on P is a simple closure space (P, C) (whose closed sets are preferably called varieties) satisfying the strong exchange axiom. Planar spaces (PS's) are the 3-DLS's. Their role is crucial because the (bottom) 3- truncation of every n-DLS with n ≥ 3 is a planar space and also because their structure, which is richer and more restricted than that of linear spaces, still allows enough freedom to include interesting and diverse spaces, such as Fischer spaces and Benz planes.
34 citations
31 citations
TL;DR: In this article, the Calderon-Lozanovski spaces between Banach function lattices and L∝ are considered and it is shown that under some general conditions these spaces posses certain monotonicity, rotundity and uniform nonsquareness properties.
25 citations
TL;DR: In this article, it was shown that for any mathematical statement about compactoids there exists an equivalent dual statement formulated in terms of Banach spaces, and conversely, an anti-equivalence between categories (Theorem 4.6).
22 citations
14 citations
TL;DR: Spaces obtained from the Besov spaces, and the Lizorkin-Triebel spaces by the real method of interpolation are investigated in this article, where the authors show how to obtain these spaces from the real data.
Abstract: Spaces obtained from the Besov spaces , and the Lizorkin-Triebel spaces by the real method of interpolation are investigated.Bibliography: 15 titles.
TL;DR: In this paper, the authors consider compact spaces defined by adequate families of sets as well as continuous images of such spaces which are called AD-compact spaces, and prove that there are nonpolyadic AD compact spaces having a strictly positive measure, and also show that some results on Banach spaces C (K ) valid for a dyadic K may be extended to K being AD compact.
TL;DR: In this article, the existence of separable r.i.d. spaces on [0, 1] containing an isomorphic copy of lp(Γ) for uncountable sets was shown.
Abstract: Given 0 2 this shows the existence of (non-trivial) separable r.i. spaces on [0, 1] containing an isomorphic copy ofLp. The discrete case of Orlicz spaces lF (I) containing an isomorphic copy of lp(Γ) for uncountable sets Γ ⊂I is also considered.
TL;DR: In this paper, the relation between real interpolation spaces (X, Y)?,? and real linear functionals (YG, XG) is investigated, and applications are given to Sobolev spaces, best approximation with constraints, and weighted Lebesgue spaces.
TL;DR: In this article, a general method for the construction of bases and unconditional finite-dimensional basis decompositions for spaces with the property of unconditional martingale differences is proposed, which makes use of a certain strongly continuous representation of Cantor's group in these spaces.
Abstract: In the paper, a general method for the construction of bases and unconditional finite-dimensional basis decompositions for spaces with the property of unconditional martingale differences is proposed. The construction makes use of a certain strongly continuous representation of Cantor's group in these spaces. The results are applied to vector function spaces and symmetric spaces of measurable operators associated with factors of type II.
Posted Content•
TL;DR: The main result of as mentioned in this paper is that every surjective isometry between two ideal Banach function spaces satisfying certain conditions can be expressed as a composition of a measurable transformation of a variable and multiplication by a function.
Abstract: The main result says that every surjective isometry between two ideal Banach function spaces satisfying certain conditions can be presented as a composition of a measurable transformation of a variable and multiplication by a function.
Journal Article•
TL;DR: In this paper, the authors discuss the concept of near smoothness in some Banach sequence spaces and propose a method to approximate the smoothness of the Banach sequences in a near smooth way.
Abstract: The aim of this paper is to discuss the concept of near smoothness in some Banach sequence spaces.
TL;DR: In this paper, the authors obtained analogous estimates for functions belonging to Orlicz or Musielak-Orlicz type spaces with respect to the canonical modular functional, where K is a homogeneous kernel and f belongs to some KSthe functional space.
Abstract: where K is a homogeneous kernel and f belongs to some KSthe functional space. In these papers the estimates are taken with respect to the KSthe norm of the space. Recently in [2] we obtained analogous estimates for functions belonging to Orlicz or Musielak-Orlicz type spaces L ~, with respect to the canonical modular functional. These results enable us to say that, for example,
TL;DR: In this paper, a continuity principle for positive linear operators in exponential type Orlicz spaces is proved, where linear operators under consideration are continuous in measure and commute with a family of measure-preserving transformations which is large enough to mix the phase space.
Abstract: A continuity principle for positive linear operators in exponential type Orlicz spaces is proved. The linear operators under consideration are continuous in measure and commute with a family of measure-preserving transformations which is large enough to mix the phase space. The method used in the proof relies upon Banach’s principle and a technique established in Stein-Sawyer’s continuity principles in spaces, and the present result may be simultaneously viewed as an extension of these results into Orlicz spaces, as well as a dominated ergodic theorem in these spaces. The essence of this duality follows from the fact that the given exponential Orlicz norms are equivalent to the associated Laurent norms. Using this fact we are also able to establish a specific form of the positive decreasing function arising in Banach’s principle for linear operators in the Orlicz spaces under our hypotheses. Moreover by using the conjugacy lemma of Halmos it is shown that a stronger version of the continuity principle is valid in the case where the operators are defined by means of a matrix summation method. An application is given to stationary ergodic sequences of random variables.
TL;DR: In this paper, the homogeneous Riemannian spaces that are closest in a definable sense to symmetric spaces are studied, i.e., the spaces that have the most symmetric properties.
Abstract: In this note we study the homogeneous Riemannian spaces that are closest in a definite sense to symmetric spaces.
01 Jan 1995
TL;DR: In this paper, a distribution is attached to a very abstract object, a random variable on a probability space, it can also be thought of as given by a Radon measure on R. The dual nature of distributions is discussed.
Abstract: In Chapter IV, we began by basing probability theory on the theory of abstract measure spaces of Chapter I. We then studied convergence in distribution by means of the Fourier transform on R d . Thus both abstract integration theory and classical analysis were necessary to obtain the limit theorems of probability theory. These two sources of Chapter IV derive from the dual nature of distributions. Although a distribution is attached to a very abstract object, a random variable on a probability space, it can also be thought of as given by a Radon measure on R. Borrowing an image from Plato, we might say that distributions have a daemonic nature: they come simultaneously from celestial objects (the abstract theory of measure spaces) and terrestrial objects (analysis on R).
01 Jan 1995
TL;DR: In this article, the notion of C-semigroup on a Banach space was introduced and proved to satisfy various functional inequalities such as Poincare inequality, logarithmical Sobolev inequality and Stein-Meyer-Bakry inequalities (Riesz transform).
Abstract: We introduce the notion of C-semigroup on a Banach space. This notion is intimately relevent to classical Dirichlet forms on Banach spaces. We shall prove a sufficient condition for a semigroup on Rd to be a C-semigroup. Then, we prove that C-semigroups satisfy various functional inequalities such as Poincare inequality, logarithmical Sobolev inequality and Stein-Meyer-Bakry inequalities (Riesz transform).