Showing papers on "Birnbaum–Orlicz space published in 1996"

Nonlinear Integral Equations in Abstract Spaces

Abstract: Preface. 1. Preliminaries. 2. Nonlinear Integral Equations in Banach Spaces. 3. Nonlinear Integro-Differential Equations in Banach Spaces. 4. Nonlinear Impulsive Integral Equations in Banach Spaces. References.

A relationship between Poincaré-type inequalities and representation formulas in spaces of homogeneous type

Abstract: The purpose of this note is to study the relationship between the validity of L1 versions of Poincare’s inequality and the existence of representation formulas for functions as (fractional) integral transforms of first-order vector fields. The simplest example of a representation formula of the type we have in mind is the following familiar inequality for a smooth, real-valued function f(x) defined on a ball B in N-dimensional Euclidean space R:

Banach spaces determined by their uniform structures

Abstract: Following results of Bourgain and Gorelik we show that the spaces l p , 1

Fundamentals of Functional Analysis

Abstract: 1. An Excursion into Set Theory. 2. Vector Spaces. 3. Convex Analysis. 4. An Excursion into Metric Spaces. 5. Multinormed and Banach Spaces. 6. Hilbert Spaces. 7. Principles of Banach Spaces. 8. Operators in Banach Spaces. 9. An Excursion into General Topology. 10. Duality and Its Applications. 11. Banach Algebras. References. Notation Index. Subject Index.

Lindelöf powers and products of function spaces

Abstract: We give criteria for finite and countable powers of a space similar to the Michael line being Lindelöf. As applications, we give examples related to Lindelöf property in products of spaces of Michael line type and in products of spaces of continuous functions on separable σ-compact spaces. All spaces considered below are assumed to be Tychonoff (= completely regular Hausdorff). We denote by Cp(X) the space of all continuous real-valued functions endowed with the topology of pointwise convergence on X ; this topology can be obtained as the restriction of the Tychonoff product topology on the set R of all real-valued functions onX to its subset C(X) (see [Arh1]). Cp(X, 2) is the subspace of Cp(X) consisting of all functions to 2 = {0, 1}. The symbols ω, R, I and C stand for the set of naturals, the real line, the segment [0, 1], and the Cantor cube 2. If P and Q are sets, then P denotes the set of all functions from Q to P ; if κ is a cardinal, then X is the κth power of X (with the Tychonoff product topology); the projection of X to its ith factor is denoted by πi. For j ∈ 2 and σ ∈ 2, denote σaj = σ ∪ {〈i, j〉} ∈ 2. The symbol c denotes the cardinality of the continuum. Polish spaces are separable completely metrizable spaces.

Surface measures in infinite-dimensional spaces

Abstract: We construct surface measures for surfaces of codimensionn≥1 in Banach spaces, and in a wide class of locally convex spaces. It is assumed that the determining function has a continuous derivative along a subspace.

On Measures of Non-Compactness in Regular Spaces

Abstract: Previous results on non-compactness obtained in [11-13] are extended to regular spaces of measurable functions, and new criteria for the a-compactness of sets and operators are proved. An application of the abstract results to elliptic boundary problems is given as well.

Some remarks on regular Banach spaces

Abstract: A Banach space E is said to be regular if every bounded linear operator from E into E' is weakly compact. This property was studied in [7, 9] under the name Property (w). In [7], using James type spaces as constructed in [4], examples were given of regular Banach spaces which fail to have weakly sequentially complete duals, answering a question raised in [9]. In this paper, we present some more results concerning the regularity of James type spaces. The study of polynomials, or more generally, analytic functions on Banach spaces leads one to consider symmetric operators on a Banach space. Recall that a bounded linear operator T : £—>£', where £ is a Banach space, is symmetric if (Tx,y) = (x, Ty) for all x,y & E. In [2], the class of Banach spaces E such that every symmetric operator from E into E' is weakly compact is found to play a useful role. Following [3], we call such spaces symmetrically regular. It is shown below that all James type spaces built on the basis of a reflexive Banach space, and all their duals, are symmetrically regular. Consequently, we obtain many examples of symmetrically regular Banach spaces which are not regular. This answers a question raised in [2, p. 83]. We use standard Banach space terminology as may be found in [8]. All subsequent results hold for both real or complex Banach spaces. For a sequence (e,) in a Banach space, [(e,)] denotes the closed linear span of (e,). If (ft is another sequence in a possibly different Banach space, we say that (e,) dominates (ft if there is a constant C such that ||2 Ojfi|| ^ C ||2)fl/e,-|| for every finitely supported scalar sequence (a,-). Two sequences are equivalent if each dominates the other. A subsymmetric sequence is an unconditional sequence which is equivalent to each of its subsequences. The author thanks Professor R. M. Aron for bringing to his attention the references [2, 3], and the question raised on p. 83 of [2].

BMOA(R, m) and capacity density Bloch spaces on hyperbolic Riemann surfaces

Abstract: We investigate a number of spaces of functions on Riemann surfaces which are related to Bloch spaces and functions of bounded mean oscillation (BMO). These spaces are defined using properties for the corresponding function spaces on the unit disk in the complex plane, and we show that, in general, different properties lead to different function spaces. We catalogue almost completely the various relationships between these spaces.

Abstract functions with continuous differences and Namioka spaces

Abstract: FUNCTIONS WITH CONTINUOUS DIFFERENCES

On a family of Wiener type spaces

Abstract: Research on Wiener type spaces was initiated by N.Wiener in [15]. A number of authors worked on these spaces or some special cases of these spaces. A kind of generalization of the Wiener's definition was given by H.Feichtinger in [2] as a Banach spaces of functions (or measures, distributions) on locally compact groups that are defined by means of the global behaviour of certain local properties of their elements. In the present paper we discussed Wiener type spaces using the spaces Aw,ωp,q(G) and Fw,ωp,q(G) (c. f. [8]) as a local component, and Lνr(G) as a global component, where w and ν are Beurling weights on G and ω is a Beurling weight on Gˆ (c. f. [13]).

Almost linearity of -bi-Lipschitz maps between real Banach spaces

Abstract: Let X and Y be real Banach spaces. A map f between X and Y is called an -bi-Lipschitz map if (1− )‖x− y‖ ≤ ‖f(x)− f(y)‖ ≤ (1 + )‖x− y‖ for all x, y ∈ X. In this note we show that if f is an -bi-Lipschitz map with f(0) = 0 from X onto Y , then f is almost linear. We also show that if f : X −→ Y is a surjective -bi-Lipschitz map with f(0) = 0, then there exists a linear isomorphism I : X → Y such that ‖I(x)− f(x)‖ ≤ E( , α)(‖x‖ + ‖x‖2−α) where E( , α)→ 0 as → 0 and 0 < α < 1.

Extension of Functions in Sobolev Spaces on Parameter Dependent Domains

Abstract: Two-sided ϵ-dependent estimates for norms of extension operators acting in Sobolev spaces on the exterior or interior of an ϵ- thin cylindrical layer are obtained. Applications to some particular domains depending on small parameters are given.

Fourier Multipliers between Weighted Anisotropic Function Spaces. Part II: Besov-Triebel Spaces

Abstract: We determine certain classes M(X ,q0 (wo), Y 11 (w1 )) of Fourier multipliers between weighted anisotropic Besov and Triebel spaces X, ,0 (wa) and 1' 11 ,qj (wi ) where p0 < 1 and w0 , w1 are weight functions of polynomial growth. To this end we refine a method based on discrete characterizations of function spaces which was introduced in Part I of the paper. Thus widely generalized versions of known results of Bui, Johnson and others are obtained in a unified way.

Inequality of spectral bound and growth bound for positive semigroups in rearrangement invariant Banach function spaces

Abstract: It is well-known that the spectral bound s(A) and the growth bound ω0(T) of a C0-semigroup T = {T (t)}t>0 with generator A need not be equal, even if the underlying space is a Hilbert space [Za] or if the semigroup is a positive semigroup on a Banach lattice [GVW]. On the other hand, it is known that s(A) = ω0(T) for positive C0-semigroups on each of the spaces L(μ), L(μ) and C0(Ω). Recently, L. Weis [We] announced a proof of the longstanding conjecture that the growth bound and the spectral bound of positive C0-semigroups on L(μ), 1 6 p <∞, coincide. Since every rearrangement invariant Banach function space with order continuous norm is an exact interpolation space between L and L∞, this suggests that it might be possible to extend Weis’s arguments to positive C0-semigroups on certain rearrangement invariant Banach function spaces. However, somewhat earlier W. Arendt [Ar] had shown that for the positive C0-semigroup T = {T (t)}t>0 on the rearrangement invariant space Lp(1,∞) ∩ Lq(1,∞), 1 6 p < q <∞, defined by

Sobolev problem in the complete scale of Banach Spaces

Abstract: In a bounded domainG ⊂ ℝ n , whose boundary is the union of manifolds of different dimensions, we study the Sobolev problem for a properly elliptic expression of order 2m. The boundary conditions are given by linear differential expressions on manifolds of different dimensions. We study the Sobolev problem in the complete scale of Banach spaces. For this problem, we prove the theorem on a complete set of isomorphisms and indicate its applications.

Nonlinear Integral Equations In Banach Spaces

Abstract: This chapter is the main part of the book. We discuss nonlinear integral equations in Banach spaces both of the Fredholm type and the Volterra type.

Lipschitz — Orlicz Spaces and the Laplace Equation

Abstract: STEIN and TAIFJLESON gave a characterization for f E Lp(IRn) to be in the spaces Lip(a, Lp) and Zyg(a, Lp) in terms of their Poisson integrals. In this paper we extend their results to Lipschitz-Orlicz spaces Lip (cp, LM) and Zygmund-Orlicz spaces Zyg (cp, LM) and to the general function cp E P instead of the power function cp(t) = ta. Such results describe the behavior of the Laplace equation in terms of the smoothness property of differences of f in Orlicz spaces LM(IR~). More general spaces hk(cp, X, q) are also considered.