Isometries of Weighted Spaces of Harmonic Functions

We investigate the isometries between weighted spaces of harmonic functions. We show that, under some mild conditions, every isometry is a composition operator. Our research shows that the structure of isometries of weighted spaces of harmonic functions is, in general, simpler than that observed for weighted spaces of holomorphic functions. Supported by MEC and FEDER Project MTM 2005-08210.     

Bounded Variation Spaces with p-Variable

In this paper, we introduce bounded variation spaces in the Wiener sense with p-variable and study some of its basic properties.     

Complementary Spaces and Multipliers of Double Fourier Series for Functions of Bounded Variation

Complementary spaces for Fourier series were introduced by G. Goes and generalized by M. Tynnov. In this paper we investigate a notion of complementary space for double Fourier series of functions of bounded variation. Various applications are given.     

Two-Sided Estimates of the $$K$$ -Functional for Spaces of Functions of Generalized Bounded Variation

Functional Analysis and Its Applications - A two-sided estimate is proposed for the $$K$$ -functional of the pair $$(C[0,1], BV(X))$$ , where $$BV(X)$$ is the space of functions of generalized...     

Banach Limits of Locally Bounded Real Functions on Hausdorff Spaces

In this paper Banach Limits are studied for locally bounded Lipschitz functions on a Hausdorff space.     

Omniscience Principles and Functions of Bounded Variation

A very weak omniscience principle is formulated, related omniscience principlesare considered, and the theorem that a function of bounded variation is the difference of two increasing functions is shown to be equivalent to the omniscience principle WLPO. It is a so shown that an arbitrary function (not necessarily strongly extensional) with located variation on an interval is the difference of two increasing functions.     

Floating Drops and Functions of Bounded Variation

A variational problem for three fluids in which gravitational and surface tension forces are in equilibrium is studied using sets of finite perimeter and functions of bounded variation. Existence theorems are proven which imply the existence of an axisymmetric floating drop. This problem has been studied previously as a free boundary problem for axisymmetric capillary surfaces by Elcrat, Neel and Siegel, but the general existence problem for arbitrary drop volumes was left open. The results presented here settle a version of this question.     

Isometries on Noncommutative Symmetric Spaces

Doklady Mathematics - Let $$\mathcal{M}$$ be an atomless semifinite von Neumann algebra equipped with a faithful normal semifinite trace τ (or else, an atomic von Neumann algebra with all...     

Spaces of Functions of Generalized Bounded Variation. II: Questions of Uniform Convergence of Fourier Series

Tests are given for uniform convergence of Fourier series for spaces of functions of generalized bounded variation; along with the well-known tests (of Salem–Oskolkov–Young, Chanturiya, and Waterman) we suggest new tests. We show that the Waterman test for uniform convergence of Fourier series is strongest and unimprovable. We present a theorem on exact estimates for the Fourier coefficients for spaces of functions of bounded variation which contains classical results, improves several well-known results, and gives some new results.     

Linear Isometries of S~p Spaces

Abstract This paper gencralizes the result about linear isometries of S~ spaces given by W.P.Novingerand D.M.Oberlin[2]for the unite dise of C to the bounded symmetric domains of C~n     

Entire Functions of Bounded Type on Fréchet Spaces

We show that holomorphic mappings of bounded type defined on Fréchet spaces extend to the bidual. The relationship between holomorphic mappings of bounded type and of uniformly bounded type is discussed and some algebraic and topological properties of the space of all entire mappings of (uniformly) bounded type are proved, for example a holomorphic version of Schauder's theorem.     

Linear Isometries of S^D Spaces

This paper generalizes the result about linear isometries of S^pspaces given by W.P.Novinger and D.M.Oberlin[2] for the unite dise of C to the bounded symmetrie domains of C^n。     

A Constructive Look at Functions of Bounded Variation

Functions with bounded variation and with a (total) variationare examined within Bishop's constructive mathematics. It isshown that the property of having a variation is hereditarydownward on compact intervals, and hence that a real-valuedfunction f with a variation on a compact interval can be expressedas a difference of two increasing functions. Moreover, if fis sequentially continuous, then the corresponding variationfunction, and hence f itself, is uniformly continuous. 1991Mathematics Subject Classification 26A45.     

Bounded Functions in Möbius Invariant Dirichlet Spaces

Forp∈(0, 1), letQ_p(Q_{p, 0}) be the space of analytic functionsfon the unit diskΔwith sup_w∈Δ ‖f°?_w‖_p<∞ (lim_|w|→1 ‖f°?_w‖_p=0), where ‖·‖_pmeans the weighted Dirichlet norm and?_wis the Möbius map ofΔonto itself with?_w(0)=w. In this paper, we prove the Corona theorem for the algebraQ_p∩H^∞(Q_{p, 0}∩H^∞); then we provide a Fefferman–Stein type decomposition forQ_p(Q_{p, 0}), and finally we describe the interpolating sequences forQ_p∩H^∞(Q_{p, 0}∩H^∞)).     

Approximate Isometries on Finite-Dimensional Normed Spaces

Every -isometry between real normed spaces of the same finitedimension which maps the origin to the origin may be uniformlyapproximated to within 2 by a linear isometry. Under a smoothnesshypothesis, necessary and sufficient conditions are obtainedfor the same conclusion to hold for a given -isometry betweeninfinite-dimensional Banach spaces. 1991 Mathematics SubjectClassification 46B04.     

Spaces of Vector-Valued Integrable Functions and Localization of Bounded Subsets

We study the structure of bounded sets in the space L¹{E} of absolutely integrable Lusin-measurable functions with values in a locally convex space E. The main idea is to extend the notion of property (B) of Pietsch, defined within the context of vector-valued sequences, to spaces of vector-valued functions. We prove that this extension, that at first sight looks more restrictive, coincides with the original property (B) for quasicomplete spaces. Then we show that when dealing with a locally convex space, property (B) provides the link to prove the equivalence between Radon–Nikodym property (the existence of a density function for certain vector measures) and the integral representation of continuous linear operators T: L¹ → E, a fact well-known for Banach spaces. We also study the relationship between Radon–Nikodym property and the characterization of the dual of L¹{E} as the space L^∞{E′_b}.     

Parabolic Differential Equations in Ordered Banach Spaces of Bounded Functions

Let A be a set, and let E be the Banach space of bounded functions : A R, equipped with its natural order. With a rectangle R = (a,b) × (0,T] let F(x,t,) : R × E E be a bounded, continuous function satisfying a local Hölder condition and being quasimonotone increasing with respect to . Then there exists a solution u: [a,b] × [0,T] E of the problem ut(x,t) – uxx(x,t) = F(x,t,u(x,t)) ((x,t) R), u(x,t) = 0 ((x,t) R R).     

A-Systems, Independent Functions, and Sets Bounded in Spaces of Measurable Functions

Let $U \subset L_o ([0,1],\mathcal{M},m)$ be a set of Lebesgue measurable functions. Suppose also that two seminormed spaces of real number sequences are given: $\mathcal{A}$ and $\mathcal{B}$ . We study $\left( {\mathcal{A},\mathcal{B}} \right)$ -sets U defined by the classes $\mathcal{A}$ and $\mathcal{B}$ as follows: $\forall a = (a_n ) \in \mathcal{A}, \forall (f_n (t)) \in u^\mathbb{N} $ (or for sequences similar to $(f_n (t))$ ) $\exists E = E(a) \subset [0,1], mE = 1$ such that $\{ a_n f_n (t)\} 1_E (t)\} \in \mathcal{B}, t \in [0,1]$ . We consider three versions of the definition of $\left( {\mathcal{A},\mathcal{B}} \right)$ -sets, one of which is based on functions independent in the probability sense. The case ${\mathcal{B}}=l_\infty$ is studied in detail. It is shown that $({\mathcal{A}},l_\infty)$ -independent sets are sets bounded or order bounded in some well-known function spaces (L _p , L _p,q , etc.) constructed with respect to the Lebesgue measure. A characterization of such sets in terms of seminormed spaces of number sequences is given. The (l ₁,c _°)- and $(\mathcal{A},l_1 )$ -sets were studied by E. M. Nikishin.