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).

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.

Composition operators on μ-Bloch spaces

2009 ◽  
Vol 61 (1) ◽  
pp. 50-75 ◽  
Author(s):  
Huaihui Chen ◽  
Paul Gauthier
Keyword(s):  
Continuous Function ◽  
Unit Ball ◽  
Composition Operator ◽  
Composition Operators ◽  
Sufficient Conditions ◽  
Positive Continuous Function ◽  
Bloch Spaces ◽  
Bloch Functions ◽  
Necessary And Sufficient

Abstract. Given a positive continuous function μ on the interval 0 < t ≤ 1, we consider the space of so-called μ-Bloch functions on the unit ball. If μ(t ) = t, these are the classical Bloch functions. For μ, we define a metric Fμz (u) in terms of which we give a characterization of μ-Bloch functions. Then, necessary and sufficient conditions are obtained in order that a composition operator be a bounded or compact operator between these generalized Bloch spaces. Our results extend those of Zhang and Xiao.

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.

Almost transitivity of some function spaces

1994 ◽  
Vol 116 (3) ◽  
pp. 475-488 ◽  
Author(s):  
Peter Greim ◽  
James E. Jamison ◽  
Anna Kamińska
Keyword(s):  
Unit Ball ◽  
Orlicz Space ◽  
Orlicz Spaces ◽  
Extreme Points ◽  
Function Spaces ◽  
Separable Spaces

AbstractThe almost transitive norm problem is studied for Lp (μ, X), C(K, X) and for certain Orlicz and Musielak-Orlicz spaces. For example if p ≠ 2 < ∞ then Lp (μ) has almost transitive norm if and only if the measure μ is homogeneous. It is shown that the only Musielak-Orlicz space with almost transitive norm is the Lp-space. Furthermore, an Orlicz space has an almost transitive norm if and only if the norm is maximal. Lp (μ, X) has almost transitive norm if Lp(μ) and X have. Separable spaces with non-trivial Lp-structure fail to have transitive norms. Spaces with nontrivial centralizers and extreme points in the unit ball also fail to have almost transitive norms.

scholarly journals Composition operators on some holomorphic Banach function spaces

2009 ◽  
Vol 104 (2) ◽  
pp. 275 ◽  
Author(s):  
A. El-Sayed Ahmed ◽  
M.A. Bakhit
Keyword(s):  
Composition Operator ◽  
Carleson Measure ◽  
Composition Operators ◽  
Bloch Space ◽  
Function Spaces ◽  
Banach Function Spaces

In this paper, we study composition operators on some Möbius invariant Banach function spaces like Bloch and $F(p,q,s)$ spaces. We give a Carleson measure characterization on $F(p,q,s)$ spaces, then we use this Carleson measure characterization of the compact compositions on $F(p,q,s)$ spaces to show that every compact composition operator on $F(p,q,s)$ spaces is compact on a Bloch space. Also, we give conditions to clarify when the converse holds.

scholarly journals -Carleson Measures for a Class of Hardy-Orlicz Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Benoît Florent Sehba
Keyword(s):  
Composition Operators ◽  
Orlicz Spaces ◽  
Integral Operators ◽  
Alternative Interpretation ◽  
Carleson Measures ◽  
Weighted Composition Operators ◽  
Weak Factorization ◽  
Type Integral ◽  
Weighted Composition

An alternative interpretation of a family of weighted Carleson measures is used to characterize -Carleson measures for a class of Hardy-Orlicz spaces admitting a nice weak factorization. As an application, we provide with a characterization of symbols of bounded weighted composition operators and Cesàro-type integral operators from these Hardy-Orlicz spaces to some classical holomorphic function spaces.

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