scholarly journals An operator characterization of Lp-spaces in a class of Orlicz spaces

2007 ◽  
Author(s):  
Maciej Burnecki
Keyword(s):  
Orlicz Spaces ◽  
Lp Spaces ◽  
Operator Characterization

A compact operator characterization of ?1

1974 ◽  
Vol 208 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Daniel J. Randtke
Keyword(s):  
Compact Operator ◽  
Operator Characterization

On approximation in Weighted Orlicz spaces

2012 ◽  
Vol 62 (1) ◽  
Author(s):  
Ali Guven ◽  
Daniyal Israfilov
Keyword(s):  
Approximation Theory ◽  
Orlicz Spaces ◽  
Trigonometric Approximation ◽  
Inverse Theorem ◽  
Lipschitz Classes

AbstractAn inverse theorem of the trigonometric approximation theory in Weighted Orlicz spaces is proved and the constructive characterization of the generalized Lipschitz classes defined in these spaces is obtained.

Extreme Positive Contractions on Finite Dimensional lp-Spaces

1985 ◽  
Vol 37 (4) ◽  
pp. 682-699 ◽  
Author(s):  
Ryszard Grząślewicz
Keyword(s):  
Measure Space ◽  
Finite Measure ◽  
Facial Structure ◽  
Positive Part ◽  
Counting Measure ◽  
Lp Spaces ◽  
Doubly Stochastic ◽  
Finite Dimensional ◽  
Finite Measure Space

In this paper we give a characterization of the extreme positive contractions on finite dimensional lp-spaces for 1 < p < ∞. This is related to the characterization of the extreme doubly stochastic operators. In Section 2 we present the basic properties of the facial structure of the set of doubly stochastic n × m matrices. In Section 3 we use these facts for description of the facial structure of the set of positive contractions on finite dimensional lp-space. Next is considered stability of the positive part of the unit ball of operators (Section 5). In Section 7 we prove that extreme positive contractions on are strongly exposed.1. Terminology and notation. Let (X, , m) be a a-finite measure space. As usual, we denote by LP(m), 1 < p < ∞, the Banach lattice of all p-summable real-valued functions on X with standard norm and order. If X = {1, 2 , …, n) n < ∞, and m is a counting measure we write instead of LP(m). If X = [0, 1] and m is Lebesgue measure we write briefly LP.

scholarly journals Carleson Measure Theorems for Large Hardy-Orlicz and Bergman-Orlicz Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Stéphane Charpentier ◽  
Benoît Sehba
Keyword(s):  
Unit Ball ◽  
Orlicz Space ◽  
Carleson Measure ◽  
Composition Operators ◽  
Orlicz Spaces ◽  
Growth Functions

We characterize those measuresμfor which the Hardy-Orlicz (resp., weighted Bergman-Orlicz) spaceHΨ1(resp.,AαΨ1) of the unit ball ofCNembeds boundedly or compactly into the Orlicz spaceLΨ2(BN¯,μ)(resp.,LΨ2(BN,μ)), when the defining functionsΨ1andΨ2are growth functions such thatL1⊂LΨjforj∈{1,2}, and such thatΨ2/Ψ1is nondecreasing. We apply our result to the characterization of the boundedness and compactness of composition operators fromHΨ1(resp.,AαΨ1) intoHΨ2(resp.,AαΨ2).

CLASSICAL PROPERTIES OF COMPOSITION OPERATORS ON HARDY–ORLICZ SPACES ON PLANAR DOMAINS

2018 ◽  
Vol 107 (02) ◽  
pp. 256-271
Author(s):  
MICHAŁ RZECZKOWSKI
Keyword(s):  
Composition Operators ◽  
Orlicz Spaces ◽  
Weak Compactness ◽  
Multiply Connected Domains ◽  
Multiply Connected ◽  
Jordan Curves ◽  
Planar Domains

In this paper we study composition operators on Hardy–Orlicz spaces on multiply connected domains whose boundaries consist of finitely many disjoint analytic Jordan curves. We obtain a characterization of order-bounded composition operators. We also investigate weak compactness and the Dunford–Pettis property of these operators.

scholarly journals A characterization of weighted Bergman-Orlicz spaces on the unit ball in Cn

2003 ◽  
Vol 74 (1) ◽  
pp. 5-18 ◽  
Author(s):  
Yasuo Matsugu ◽  
Jun Miyazawa
Keyword(s):  
Convex Function ◽  
Unit Ball ◽  
Lebesgue Measure ◽  
Orlicz Space ◽  
Positive Constant ◽  
Real Line ◽  
Orlicz Spaces ◽  
Holomorphic Functions ◽  
Strongly Convex

AbstractLet B denote the unit ball in Cn, and ν the normalized Lebesgue measure on B. For α > −1, define Here cα is a positive constant such that να(B) = 1. Let H(B) denote the space of all holomorphic functions in B. For a twice differentiable, nondecreasing, nonnegative strongly convex function ϕ on the real line R, define the Bergman-Orlicz space Aϕ(να) by In this paper we prove that a function f ∈ H(B) is in Aϕ(να) if and only if where is the radial derivative of f.

scholarly journals Characterization of generalized Orlicz spaces

2018 ◽  
Vol 22 (02) ◽  
pp. 1850079 ◽  
Author(s):  
Rita Ferreira ◽  
Peter Hästö ◽  
Ana Margarida Ribeiro
Keyword(s):  
Sobolev Space ◽  
Sobolev Spaces ◽  
Variable Exponent ◽  
Orlicz Spaces ◽  
Difference Quotient ◽  
Variable Exponent Spaces ◽  
The Difference ◽  
Fractional Smoothness

The norm in classical Sobolev spaces can be expressed as a difference quotient. This expression can be used to generalize the space to the fractional smoothness case. Because the difference quotient is based on shifting the function, it cannot be used in generalized Orlicz spaces. In its place, we introduce a smoothed difference quotient and show that it can be used to characterize the generalized Orlicz–Sobolev space. Our results are new even in Orlicz spaces and variable exponent spaces.

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