Showing papers on "Birnbaum–Orlicz space published in 1989"

Convex Functions, Monotone Operators and Differentiability

Abstract: Convex functions on real Banach spaces.- Monotone operators, subdifferentials and Asplund spaces.- Lower semicontinuous convex functions.- Smooth variational principles, Asplund spaces, weak Asplund spaces.- Asplund spaces, the RNP and perturbed optimization.- Gateaux differentiability spaces.- A generalization of monotone operators: Usco maps.

Non-commutative Banach Function Spaces

Abstract: In this paper we survey some aspects of the theory of non-commutative Banach function spaces, that is, spaces of measurable operators associated with a semi- finite von Neumann algebra. These spaces are also known as non-commutative symmetric spaces. The theory of such spaces emerged as a common generalization of the theory of classical (“commutative”) rearrangement invariant Banach function spaces (in the sense of W.A.J. Luxemburg and A.C. Zaanen) and of the theory of symmetrically normed ideals of bounded linear operators in Hilbert space (in the sense of I.C. Gohberg and M.G. Krein). These two cases may be considered as the two extremes of the theory: in the first case the underlying von Neumann algebra is the commutative algebra L ∞ on some measure space (with integration as trace); in the second case the underlying von Neumann algebra is B (ℌ), the algebra of all bounded linear operators on a Hilbert space ℌ (with standard trace). Important special cases of these non-commutative spaces are the non-commutative L p-spaces, which correspond in the commutative case with the usual L p-spaces on a measure space, and in the setting of symmetrically normed operator ideals they correspond to the Schatten p-classes \( \mathfrak{S}_p \) .

Lifting results for sequences in Banach spaces

Abstract: Several important classes of Banach spaces are characterized by means of convergence properties of sequences. For example, if X is a Banach space, then X belongs to the class Nl1 of spaces without copies of l1, the class R of reflexive spaces or the class F of finite-dimensional spaces if and only if each bounded sequence has respectively a weakly Cauchy (w-Cauchy), weakly convergent (w-convergent) or convergent subsequence. Similarly X is in the class WSC of weakly sequentially complete spaces, or the class SCH of spaces with the Schur property if and only if each w-Cauchy sequence is w-convergent, or convergent, respectively; note that X ∈ SCH if and only if each w-convergent sequence of X is convergent (see [12], p. 47).

Uniformly non-l n (1) Musielak-Orlicz Spaces of Bochner Type

Abstract: It is proved that in the case of a non-atomic measure μ a Musielak-Orlicz space L?(μ, X) of Bochner type is uniformly non-/i if and only if both spaces £(μ, R) and X are uniformly non-/**. These results generalize the results of [4], [7] and [8] and are connected also with some results of [3]. 1980 Mathematics Subject Classification (1985 Revision): 46E30, 46E40.

Initial Value Problems in Banach Spaces

Abstract: The goal of this introductory chapter is not only to solve initial value problems in Banach spaces but also to prove some of the statements necessary for the further constructions.

Evolution equations and scales of Banach spaces

Abstract: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.

Imbedding theorems of Besov spaces in Banach lattices

Abstract: The paper examines imbeddings of Besov spaces B E, θ ω in ideal spaces (Banach lattices) given that ω ∈ Sk). In particular, the symmetric hull of the space B E, θ ω is described (E is a symmetric space), an inequality of different metrics is obtained, and imbeddings in Orlicz and Lorentz spaces and in some weighted spaces are studied. Most of the results are easily extended to the anisotropic case.

Interpolation between Sobolev and between Lipschitz spaces of analytic functions on starshaped domains

Abstract: We show that on a starshaped domain Q in Cn (actually on a somewhat larger, biholomorphically invariant class) the YP-Sobolev spaces of analytic functions form an interpolation scale for both the real and complex methods, for each p, 0 < p < oo . The case p = oo gives the Lipschitz scale; here the functor (, )[0 has to be considered (rather than (, )[01) .

On the generalized Lagrange spaces with the metric γij(x)+(1/c2)yiyj

Abstract: In this paper we shall study the spaces M n . Among the many interesting results which have obtained it is to be remarked that the spaces M n are not reducible to Lagrange spaces and so neither to Finslerian spaces or Riemannian spaces

Continuity of operators in spaces of vector functions, with applications to the theory of bases

Abstract: Banach spaces with unconditional martingale differences are investigated. In Sec. 1 a survey of their fundamental properties and connections with vector-valued harmonic analysis is given. In Sec. 2 new results are obtained regarding bases in the spaces E(X), where E is a symmetric space.

Interpolation of linear operators in the Köthe dual spaces

Abstract: In this paper we investigate when the Kothe dual spaces Y′ and X′ are interpolation spaces with respect to couples of the Kothe dual spaces (Y′0, Y′1) and (X′0, X′1), respectively, where X and Y are interpolation spaces with respect to given couples (X0,X1) and (Y0, Y1 of Banach function spaces.

Totally characteristic pseudo-differential operators in Besov-Lizorkin-Triebel spaces

Abstract: A full symbolic calculus for totally characteristic pseudo-differential operators acting in general scales of function spaces with conormal asymptotics of several types will be developed. By using modified methods we will show that the results of S. Rempel and B.-W. Schulze for full asymptotics in Sobolev spaces can be generalized for Besov-Lizorkin-Triebel spaces, in particular, Holder spaces, with other types of asymptotics.

On Smallest and Largest Orlicz Spaces

Abstract: There are found the smallest and largest spaces among all ORLICZ spaces generated by non-decreasing ORLICZ functions and also among all ORLICZ spaces generated by s-convex ORLICZ functions, 0 < s ⩽ 1.

Sobolev Spaces and Their Basic Properties

Abstract: This chapter is concerned with the fundamental properties of Sobolev spaces including the Sobolev inequality and its associated imbedding theorems. The basic Sobolev inequality is proved in two ways, one of which employs the co-area formula (Section 2.7) to obtain the best constant in the inequality. This method relates the Sobolev inequality to the isoperimetric inequality.

On the banach spaces in which martingale difference sequences are unconditional

Abstract: We gave two characterizations of the Banach spaces which have the UMD pro-perty are presented by using the convex Φ-function inequalities of B-valued martin-gales and their transforms,it is proved that the vector=valued Orlicz spaces L_Φ(X)and X have the UMD property simultaneously when Φ∈Δ_2∩▽_2;in particular,thescalar-valued Orlicz spaces L_Φ have UMD property iff Φ∈Δ_2∩▽_2.

Embedding of Sobolev Spaces into Lipschitz Spaces

Abstract: The main result of the paper is that if Ω is a bounded uniform domain in ℝn and p>n, then the Sobolev space Wl, p(Ω) embeds continously into Cα(Ω), α = 1 - n/p.