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New examples of K-monotone weighted Banach couples

Sergey V. Astashkin, Lech Maligranda, Konstantin E. Tikhomirov (2013)

Studia Mathematica

Some new examples of K-monotone couples of the type (X,X(w)), where X is a symmetric space on [0,1] and w is a weight on [0,1], are presented. Based on the property of w-decomposability of a symmetric space we show that, if a weight w changes sufficiently fast, all symmetric spaces X with non-trivial Boyd indices such that the Banach couple (X,X(w)) is K-monotone belong to the class of ultrasymmetric Orlicz spaces. If, in addition, the fundamental function of X is t 1 / p for some p ∈ [1,∞], then X = L p . At...

Nonconvolution transforms with oscillating kernels that map 1 0 , 1 into itself

G. Sampson (1993)

Studia Mathematica

We consider operators of the form ( Ω f ) ( y ) = ʃ - Ω ( y , u ) f ( u ) d u with Ω(y,u) = K(y,u)h(y-u), where K is a Calderón-Zygmund kernel and h L (see (0.1) and (0.2)). We give necessary and sufficient conditions for such operators to map the Besov space 1 0 , 1 (= B) into itself. In particular, all operators with h ( y ) = e i | y | a , a > 0, a ≠ 1, map B into itself.

Nonlinear operators of integral type in some function spaces.

Carlo Bardaro, Gianluca Vinti, J. Musielak (1997)

Collectanea Mathematica

We give results about embeddings, approximation and convergence theorems for a class of general nonlinear operators of integral type in abstract modular function spaces. Thus we extend some previous result on the matter.

Non-Newtonian fluids and function spaces

Růžička, Michael, Diening, Lars (2007)

Nonlinear Analysis, Function Spaces and Applications

In this note we give an overview of recent results in the theory of electrorheological fluids and the theory of function spaces with variable exponents. Moreover, we present a detailed and self-contained exposition of shifted N -functions that are used in the studies of generalized Newtonian fluids and problems with p -structure.

Non-similarity of Walsh and trigonometric systems

P. Wojtaszczyk (2000)

Studia Mathematica

We show that in L p for p ≠ 2 the constants of equivalence between finite initial segments of the Walsh and trigonometric systems have power type growth. We also show that the Riemann ideal norms connected with those systems have power type growth.

Normability of gamma spaces

Filip Soudský (2016)

Commentationes Mathematicae Universitatis Carolinae

We give a full characterization of normability of Lorentz spaces Γ w p . This result is in fact known since it can be derived from Kamińska A., Maligranda L., On Lorentz spaces, Israel J. Funct. Anal. 140 (2004), 285–318. In this paper we present an alternative and more direct proof.

Normability of Lorentz spaces—an alternative approach

Amiran Gogatishvili, Filip Soudský (2014)

Czechoslovak Mathematical Journal

We study normability properties of classical Lorentz spaces. Given a certain general lattice-like structure, we first prove a general sufficient condition for its associate space to be a Banach function space. We use this result to develop an alternative approach to Sawyer’s characterization of normability of a classical Lorentz space of type Λ . Furthermore, we also use this method in the weak case and characterize normability of Λ v . Finally, we characterize the linearity of the space Λ v by a simple...

Normal structure and weakly normal structure of Orlicz spaces

Shutao Chen, Yanzheng Duan (1991)

Commentationes Mathematicae Universitatis Carolinae

Every Orlicz space equipped with Orlicz norm has weak sum property, therefore, it has weakly normal structure and fixed point property. A criterion of sum property also of normal structure for such spaces is given as well, which shows that every Orlicz space has isonormal structure.

Normal structure of Lorentz-Orlicz spaces

Pei-Kee Lin, Huiying Sun (1997)

Annales Polonici Mathematici

Let ϕ: ℝ → ℝ₊ ∪ 0 be an even convex continuous function with ϕ(0) = 0 and ϕ(u) > 0 for all u > 0 and let w be a weight function. u₀ and v₀ are defined by u₀ = supu: ϕ is linear on (0,u), v₀=supv: w is constant on (0,v) (where sup∅ = 0). We prove the following theorem. Theorem. Suppose that Λ ϕ , w ( 0 , ) (respectively, Λ ϕ , w ( 0 , 1 ) ) is an order continuous Lorentz-Orlicz space. (1) Λ ϕ , w has normal structure if and only if u₀ = 0 (respectively, v ϕ ( u ) · w < 2 a n d u < ) . (2) Λ ϕ , w has weakly normal structure if and only if 0 v ϕ ( u ) · w < 2 .

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