New bounds for weights.
Radice, Teresa (2008)
Annales Academiae Scientiarum Fennicae. Mathematica
Jenkins, Russell S., Garimella, Ramesh V. (2000)
International Journal of Mathematics and Mathematical Sciences
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 for some p ∈ [1,∞], then . At...
P. N. Dowling, C. J. Lennard, B. Turett (2007)
Studia Mathematica
We show that every subset of L¹[0,1] that contains the nontrivial intersection of an order interval and finitely many hyperplanes fails to have the fixed point property for nonexpansive mappings.
L. Greco, T. Iwaniec (1994)
Annales de l'I.H.P. Analyse non linéaire
Oscar Blasco, Alberto Ruiz, Luis Vega (1999)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Ryszard Frankiewicz, Grzegorz Plebanek (1994)
Studia Mathematica
Jutta Schmeisser (1981)
Czechoslovak Mathematical Journal
G. Sampson (1993)
Studia Mathematica
We consider operators of the form with Ω(y,u) = K(y,u)h(y-u), where K is a Calderón-Zygmund kernel and (see (0.1) and (0.2)). We give necessary and sufficient conditions for such operators to map the Besov space (= B) into itself. In particular, all operators with , a > 0, a ≠ 1, map B into itself.
Enrique Lami-Dozo, Philippe Turpin (1987)
Studia Mathematica
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.
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 -functions that are used in the studies of generalized Newtonian fluids and problems with -structure.
P. Wojtaszczyk (2000)
Studia Mathematica
We show that in 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.
Shang, Shaoqiang, Cui, Yunan, Fu, Yongqiang (2011)
Abstract and Applied Analysis
Filip Soudský (2016)
Commentationes Mathematicae Universitatis Carolinae
We give a full characterization of normability of Lorentz spaces . 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.
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 . Furthermore, we also use this method in the weak case and characterize normability of . Finally, we characterize the linearity of the space by a simple...
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.
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 (respectively, ) is an order continuous Lorentz-Orlicz space. (1) has normal structure if and only if u₀ = 0 (respectively, (2) has weakly normal structure if and only if .
Eleni Katirtzoglou (1997)
Collectanea Mathematica
Shekhtman, Boris, Skrzypek, LesŁaw (2006)
Abstract and Applied Analysis