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On some density theorems in regular vector lattices of continuous functions.

Francesco Altomare, Mirella Cappelletti Montano (2007)

Collectanea Mathematica

In this paper, we establish some density theorems in the setting of particular locally convex vector lattices of continuous functions de ned on a locally compact Hausdorff space, which we introduced and studied in [3,4] and which we named regular vector lattices. In this framework, by using properties of the subspace of the so-called generalized af ne functions, we give a simple description of the closed vector sublattice, the closed Stone vector sublattice and the closed subalgebra generated by...

On some equivalent geometric properties in the Besicovitch-Orlicz space of almost periodic functions with Luxemburg norm

Fazia Bedouhene, Mohamed Morsli, Mannal Smaali (2010)

Commentationes Mathematicae Universitatis Carolinae

The paper is concerned with the characterization and comparison of some local geometric properties of the Besicovitch-Orlicz space of almost periodic functions. Namely, it is shown that local uniform convexity, H -property and strict convexity are all equivalent. In our approach, we first prove some metric type properties for the modular function associated to our space. These are then used to prove our main equivalence result.

On some ergodic properties for continuous and affine functions

Charles J. K. Batty (1978)

Annales de l'institut Fourier

Two problems posed by Choquet and Foias are solved:(i) Let T be a positive linear operator on the space C ( X ) of continuous real-valued functions on a compact Hausdorff space X . It is shown that if n - 1 r = 0 n - 1 T r 1 converges pointwise to a continuous limit, then the convergence is uniform on X .(ii) An example is given of a Choquet simplex K and a positive linear operator T on the space A ( K ) of continuous affine real-valued functions on K , such that inf { ( T n 1 ) ( x ) : n } < 1 for each x in K , but T n 1 does not converge to 0.

On some geometric properties of certain Köthe sequence spaces

Yunan Cui, Henryk Hudzik, Tao Zhang (1999)

Mathematica Bohemica

It is proved that if a Kothe sequence space X is monotone complete and has the weakly convergent sequence coefficient WCS ( X ) > 1 , then X is order continuous. It is shown that a weakly sequentially complete Kothe sequence space X is compactly locally uniformly rotund if and only if the norm in X is equi-absolutely continuous. The dual of the product space ( i = 1 X i ) Φ of a sequence of Banach spaces ( X i ) i = 1 , which is built by using an Orlicz function Φ satisfying the Δ 2 -condition, is computed isometrically (i.e. the exact...

On some properties for dual spaces of Musielak-Orlicz function spaces

Zenon Zbąszyniak (2011)

Banach Center Publications

We will present relationships between the modular ρ* and the norm in the dual spaces ( L Φ ) * in the case when a Musielak-Orlicz space L Φ is equipped with the Orlicz norm. Moreover, criteria for extreme points of the unit sphere of the dual space ( L Φ ) * will be presented.

On some properties of the functions from Sobolev-Morrey type spaces

Alik Najafov (2005)

Open Mathematics

In this paper the spaces of type Sobolev-Morrey-W p,a,г,τl(Q,G)-are constructed, the differential properties are studied and it is proved that the functions from these spaces satisfy Holder's condition, in the case, if the domain G∋R n satisfies the flexible λ-horn condition.

On some spaces of holomorphic functions of exponential growth on a half-plane

Marco M. Peloso, Maura Salvatori (2016)

Concrete Operators

In this paper we study spaces of holomorphic functions on the right half-plane R, that we denote by Mpω, whose growth conditions are given in terms of a translation invariant measure ω on the closed half-plane R. Such a measure has the form ω = ν ⊗ m, where m is the Lebesgue measure on R and ν is a regular Borel measure on [0, +∞). We call these spaces generalized Hardy–Bergman spaces on the half-plane R. We study in particular the case of ν purely atomic, with point masses on an arithmetic progression...

On some structural properties of Banach function spaces and boundedness of certain integral operators

T. S. Kopaliani (2004)

Czechoslovak Mathematical Journal

In this paper the notions of uniformly upper and uniformly lower -estimates for Banach function spaces are introduced. Further, the pair ( X , Y ) of Banach function spaces is characterized, where X and Y satisfy uniformly a lower -estimate and uniformly an upper -estimate, respectively. The integral operator from X into Y of the form K f ( x ) = ϕ ( x ) 0 x k ( x , y ) f ( y ) ψ ( y ) d y is studied, where k , ϕ , ψ are prescribed functions under some local integrability conditions, the kernel k is non-negative and is assumed to satisfy certain additional...

On some subspaces of Morrey-Sobolev spaces and boundedness of Riesz integrals

Mouhamadou Dosso, Ibrahim Fofana, Moumine Sanogo (2013)

Annales Polonici Mathematici

For 1 ≤ q ≤ α ≤ p ≤ ∞, ( L q , l p ) α is a complex Banach space which is continuously included in the Wiener amalgam space ( L q , l p ) and contains the Lebesgue space L α . We study the closure ( L q , l p ) c , 0 α in ( L q , l p ) α of the space of test functions (infinitely differentiable and with compact support in d ) and obtain norm inequalities for Riesz potential operators and Riesz transforms in these spaces. We also introduce the Sobolev type space W ¹ ( ( L q , l p ) α ) (a subspace of a Morrey-Sobolev space, but a superspace of the classical Sobolev space W 1 , α ) and obtain...

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