Showing papers on "Birnbaum–Orlicz space published in 1991"

Theory of Orlicz spaces

Abstract: A reference/text for mathematicians or students involved in analysis, differential equations, probability theory, and the study of integral operators where only Lebesgue spaces were used in the past. Updates and extends the pioneering work by Krasnosel'skii and Rutickii in their 1958 treatise on Orl

Comparison of Orlicz-Lorentz spaces

Abstract: Orlicz-Lorentz spaces provide a common generalization of Orlicz spaces and Lorentz spaces. They have been studied by many authors, including Masty\l o, Maligranda, and Kami\'nska. In this paper, we consider the problem of comparing the Orlicz-Lorentz norms, and establish necessary and sufficient conditions for them to be equivalent. As a corollary, we give necessary and sufficient conditions for a Lorentz-Sharpley space to be equivalent to an Orlicz space, extending results of Lorentz and Raynaud. We also give an example of a rearrangement invariant space that is not an Orlicz-Lorentz space.

On approximation by polynomials in Orlicz spaces

Abstract: In this paper, we prove Jackson theorem of derivative type in Orlicz spaces, and the results of this paper are generalization of the results of A-RK Ramazanov in [2]

Landau type theorem for Orlicz spaces

Abstract: In this paper the authors discuss Landau's theorem presenting an inverse of the classical Holder-type inequality for sequence and function spaces.The results given are for Orlicz spaces and their g ...

Sobolev spaces of infinite order

Abstract: CONTENTS Introduction ??1. Non-triviality of Sobolev spaces of infinite order ??2. Sobolev spaces of infinite order as monotonic limits of Banach spaces ??3. Embedding theorems ??4. Traces and extensions ??5. Applications Conclusion References

Complex interpolation of quasi-Banach spaces with an A-convex containing space

Abstract: Complex interpolation of general couples (X0, X1) of quasi-Banach spaces has been considered by several authors [8], [11], [16]. The first approach was made by Rivi6re in his thesis [16] and recently it has been developed by Cwikel, Milman and Sagher in [8], where some new interpolation results have been obtained. See also [9] and [17]. These authors have used in the classical construction of Calder6n (see [4] or [3]) the space ~ of all functions J(z) =~=lfk(z)xk, where x ~ X0 n X 1 and f~E A (S, C), the class of scalar valued functions analytic on the strip S={z: 0 < R e z < l } and continuous and bounded on S. As a result, a quasi-normed space of analytic functions is obtained in which the quasi-norm IL\" IL~ on ~ is the one introduced by Calder6n [4], i.e.

Some Banach space embeddings of classical function spaces

Abstract: Banach space embeddings of the Orlicz space Lp + Lq and the Lorentz space Lp, q into the Lebesgue-Bochner space Lr(ls) are demonstrated for appropriate ranges of the parameters.

Sobolev spaces in the generalized distribution spaces of Beurling type

Abstract: hh=\ Rn\^)\eiw^d$ 0. The space 2)^(0) equipped with the inductive limit topology, as 2){Q), is Frechet and we call ^{Q), the dual of WJ^Q), the Beurling's generalized distributionspace. They denote by GJ^Q) the set of all complex valued functions ^.S)S.Q') for all IUfor every X>0 and every (Q) which have compact support contained in Q. They also extend the Schwartz space denoting by Sw the space of all C°°-function (j>in L\Rn) with the property that for each multi-index a and each non-negative number A

Traces on curves of Sobolev spaces of holomorphic functions

Abstract: where S denotes the boundary of B\" and da its Lebesgue measure. It is well-known (see [5] and [6]) that in case ]~ is an integer one can use R a instead o f D a and if fCH~ then all derivatives up to order ]~ of f belong to H\" (i.e. they are in LP(S)), and thus H~ can be thought as the analogue of the Sobolev and potential spaces in real analysis. The space H~ has been the subject of several recent papers and a theory of holomorphic Sobolev spaces is being systematically developed, in many aspects analogous to the real-variable theory of Sobolev and potential spaces (see [5], [7], [12], [14], [1], [2], [3] and the forthcoming book [6]). The object of this paper is to describe the trace of the spaces H~ along certain submanifolds of S, i.e. to find the analogue of the \"trace theorem\" (see [8] or [16]). To simplify the exposition, here and in the main part of the paper, we will limit ourselves to (simple) closed smooth curves F on S and to the regular range

On asymptotically normable Fréchet spaces

Abstract: Let E be a Frechet space, a fundamental system of seminorms on E and U, for every k . E is called asymptotically normable, if there is a , such that for every , there is a p so that the seminorms and define equivalent topologies on . It is easy to see that in this case , is in fact a norm. This class of spaces appears in investigations about the structure of Frechet spaces and about the behaviour of their operators as a natural counterpart of the class of quasi-normable spaces introduced by Grothendieck [4].While the quasi-normable Frechet spaces E are those which admit an -type condition (see[7]) and for which there exists a nontrivial Frechet space F with (see [8], [9], [13], [14]), the asymptotically normable Frechet spaces E are those which admit a DN-type condition (see [13] and below) and for which there exists a nontrivial Frechet space F with . Nontrivial here could mean: an infinite dimensional nuclear Kothe space. In [7] it is shown that the quasi-normable spaces are the quotient spaces of standard spaces of the form where E is a Banach space and a matrix with for all k and We show that the asymptotically normable spaces are the subspaces of these standard spaces. They are the smallest class of Frechet spaces which contains the nuclear Kothe spaces with continuous norm, the Banach spaces and is closed under -tensor products and subspaces.The main tool for that is Theorem 3.3. For Schwartz spaces asymptotic normability coincides with countable normability in the sense of Gelfand-Shilov. We show by an example that this even for Montel spaces is not the case.

Besov spaces on surfaces with singularities

Abstract: The trace to the boundary of a domain Ω of functions in Besov spaces and Sobolev spaces defined in Ω is characterized, in the case when the boundary has singularities of a certain type.

Martingale spaces and geometrical properties of banach spaces

Abstract: In this paper some inequalities for maximal operator and p-power operator of martin-gales with values in Banach spaces are established. We discuss some relationships betweenseveral martingale spaces, and present characterizations of convexity and smoothness ofBanach spaces.

Optimality Conditions For Lipschitz Functions On Banach Spaces

Abstract: $Ab8tract$ . In convex $analysi8$ , if a convex function $f$ defined on a Banach spaoe X $attain8$ its minimum at $x_{0}$ , then $0\in ff(x_{0})$ , the subdifferential of $f$ at $x_{0}$ . Thus we study in this paper for optimality conditions of a minimization problem of locally Lipschitz objective subject to an inequality and equality constraints with values in Banach spaces. We replaoe $f$ by the Lagrangian $L$ for a given programming problem, and prove that the $Kuhn-Tucker/Fritz$ John multiplier rule holds. That is,

Integral Representation of Functionals Defined on Sobolev Spaces

Abstract: We give an integral representation result for functionals defined on Sobolev spaces; more precisely, for a functional F, we find necessary and sufficient conditions that imply the integral representation formula $$ F(u,\,B) = \int_B {f(x,\,Du)\,dx} $$

Inductive limit topologies on Orlicz spaces

Abstract: Let L be an Orlicz space defined by a convex Orlicz function φ and let E be the space of finite elements in L (= the ideal of all elements of order continuous norm). We show that the usual norm topology Tφ on L restricted to E can be obtained as an inductive limit topology with respect to some family of other Orlicz spaces. As an application we obtain a characterization of continuity of linear operators defined on E.