scholarly journals Explicit Bounds and Sharp Results for the Composition Operators Preserving the Exponential Class

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Fernando Farroni ◽  
Raffaella Giova
Keyword(s):  
Quasiconformal Mapping ◽  
Composition Operator ◽  
Composition Operators ◽  
Higher Dimensions ◽  
Related Question ◽  
Explicit Bound ◽  
Integrable Functions ◽  
Explicit Bounds ◽  
Area Distortion

Letf:Ω⊂Rn→Rnbe aquasiconformal mappingwhose Jacobian is denoted byJfand letEXP(Ω)be the space of exponentially integrable functions onΩ. We give an explicit bound for the norm of the composition operatorTf:u∈EXP(Ω)↦u∘f-1∈EXP(f(Ω))and, as a related question, we study the behaviour of the norm oflog⁡Jfin the exponential class. TheA∞property ofJfis the counterpart in higher dimensions of the area distortion formula due to Astala in the plane and it is the key tool to prove the sharpness of our results.

Composition operators on W 1 X are necessarily induced by quasiconformal mappings

2014 ◽  
Vol 12 (8) ◽  
Author(s):  
Luděk Kleprlík
Keyword(s):  
Quasiconformal Mapping ◽  
Function Space ◽  
Composition Operator ◽  
Composition Operators ◽  
Invariant Function ◽  
Quasiconformal Mappings ◽  
Open Set ◽  
Scaling Property

AbstractLet Ω ⊂ ℝn be an open set and X(Ω) be any rearrangement invariant function space close to L q(Ω), i.e. X has the q-scaling property. We prove that each homeomorphism f which induces the composition operator u ↦ u ℴ f from W 1 X to W 1 X is necessarily a q-quasiconformal mapping. We also give some new results for the sufficiency of this condition for the composition operator.

Explicit Bounds for Composition Operators Preserving BMO(ℝ)

2007 ◽  
Vol 14 (1) ◽  
pp. 21-32
Author(s):  
Teresa Alberico ◽  
Rossella Corporente ◽  
Carlo Sbordone
Keyword(s):  
Recent Result ◽  
Composition Operators ◽  
Explicit Bound ◽  
Explicit Bounds

Abstract We improve a recent result of Y. Gotoh [Pacific J. Math 201: 289-307, 2001] who has established a precise relation between the constants in P. W. Jones theorem [Ark. Mat. 21: 229-231, 1983] about homeomorphisms of the line preserving BMO. We also give an explicit bound for a distance to L ∞ after composition.

scholarly journals A Note on Unbounded Hyponormal Composition Operators inL2-Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Piotr Budzyński
Keyword(s):  
Composition Operator ◽  
Composition Operators

We construct an unbounded hyponormal composition operatorCϕinL2-space such that the domains ofCϕ2andCϕ2are trivial.

scholarly journals Some results on isometric composition operators on Lipschitz spaces

2021 ◽  
Author(s):  
Abraham Rueda Zoca
Keyword(s):  
Convex Hull ◽  
Composition Operator ◽  
Metric Spaces ◽  
Composition Operators ◽  
Extreme Points ◽  
Necessary Condition ◽  
Closed Convex Hull ◽  
Lipschitz Spaces ◽  
Complete Characterisation

AbstractGiven two metric spaces M and N we study, motivated by a question of N. Weaver, conditions under which a composition operator $$C_\phi :{\mathrm {Lip}}_0(M)\longrightarrow {\mathrm {Lip}}_0(N)$$ C ϕ : Lip 0 ( M ) ⟶ Lip 0 ( N ) is an isometry depending on the properties of $$\phi $$ ϕ . We obtain a complete characterisation of those operators $$C_\phi $$ C ϕ in terms of a property of the function $$\phi $$ ϕ in the case that $$B_{{\mathcal {F}}(M)}$$ B F ( M ) is the closed convex hull of its preserved extreme points. Also, we obtain necessary condition for $$C_\phi $$ C ϕ being an isometry in the case that M is geodesic.

scholarly journals COMPOSITION OPERATORS BELONGING TO SCHATTEN CLASS 𝒮p

2010 ◽  
Vol 81 (3) ◽  
pp. 465-472
Author(s):  
CHENG YUAN ◽  
ZE-HUA ZHOU
Keyword(s):  
Bergman Space ◽  
Composition Operator ◽  
Unit Disc ◽  
Composition Operators ◽  
Schatten Class

AbstractWe investigate the composition operators Cφ acting on the Bergman space of the unit disc D, where φ is a holomorphic self-map of D. Some new conditions for Cφ to belong to the Schatten class 𝒮p are obtained. We also construct a compact composition operator which does not belong to any Schatten class.

scholarly journals Composition operators in Orlicz spaces

2004 ◽  
Vol 76 (2) ◽  
pp. 189-206 ◽  
Author(s):  
Yunan Cui ◽  
Henryk Hudzik ◽  
Romesh Kumar ◽  
Lech Maligranda
Keyword(s):  
Composition Operator ◽  
Measure Space ◽  
Composition Operators ◽  
Orlicz Spaces

AbstractComposition operators Cτ between Orlicz spaces Lϕ (Ω, Σ, μ) generated by measurable and nonsingular transformations τ from Ω into itself are considered. We characterize boundedness and compactness of the composition operator between Orlicz spaces in terms of properties of the mapping τ, the function ϕ and the measure space (Ω, Σ, μ). These results generalize earlier results known for Lp-spaces.

scholarly journals M-Cohyponormal powers of composition operators

1992 ◽  
Vol 53 (1) ◽  
pp. 9-16
Author(s):  
Satish K. Khurana ◽  
Babu Ram
Keyword(s):  
Composition Operator ◽  
Measure Space ◽  
Composition Operators ◽  
Finite Measure ◽  
Finite Measure Space ◽  
Positive Integers ◽  
Nikodym Derivative

AbstractLet T1, i = 1, 2 be measurable transformations which define bounded composition operators C Ti on L2 of a σ-finite measure space. Let us denote the Radon-Nikodym derivative of with respect to m by hi, i = 1, 2. The main result of this paper is that if and are both M-hyponormal with h1 ≤ M2(h2 o T2) a.e. and h2 ≤ M2(h1 o T1) a.e., then for all positive integers m, n and p, []* is -hyponormal. As a consequence, we see that if is an M-hyponormal composition operator, then is -hyponormal for all positive integers n.

scholarly journals Geometric properties of composition operators belonging to Schatten classes

2001 ◽  
Vol 26 (4) ◽  
pp. 239-248 ◽  
Author(s):  
Yongsheng Zhu
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Composition Operator ◽  
Composition Operators ◽  
Schatten Classes ◽  
Geometric Properties ◽  
Image Domain ◽  
Function Mapping

We investigate the connection between the geometry of the image domain of an analytic function mapping the unit disk into itself and the membership of the composition operator induced by this function in the Schatten classes. The purpose is to provide solutions to Lotto's conjectures and show a new compact composition operator which is not in any of the Schatten classes.

Hypercyclic, mixing, and chaotic C0-semigroups induced by semiflows

2007 ◽  
Vol 27 (5) ◽  
pp. 1599-1631 ◽  
Author(s):  
T. KALMES
Keyword(s):  
Composition Operators ◽  
Continuous Functions ◽  
Weighted Composition Operators ◽  
Integrable Functions ◽  
Spaces Of Continuous Functions ◽  
Weighted Composition ◽  
Topologically Mixing

AbstractWe characterize when C0-semigroups induced by semiflows are hypercyclic, topologically mixing, or chaotic both on spaces of integrable functions and on spaces of continuous functions. Furthermore, we give characterizations of transitivity for weighted composition operators on these spaces.

Composition operators on weighted spaces of holomorphic functions on the upper half plane

2018 ◽  
Vol 122 (1) ◽  
pp. 141
Author(s):  
Wolfgang Lusky
Keyword(s):  
Half Plane ◽  
Composition Operator ◽  
Unit Disc ◽  
Composition Operators ◽  
Bounded Operator ◽  
Holomorphic Functions ◽  
Weighted Spaces ◽  
Weight Functions ◽  
Spaces Of Holomorphic Functions ◽  
Upper Half Plane

We consider moderately growing weight functions $v$ on the upper half plane $\mathbb G$ called normal weights which include the examples $(\mathrm{Im} w)^a$, $w \in \mathbb G$, for fixed $a > 0$. In contrast to the comparable, well-studied situation of normal weights on the unit disc here there are always unbounded composition operators $C_{\varphi }$ on the weighted spaces $Hv(\mathbb G)$. We characterize those holomorphic functions $\varphi \colon \mathbb G \rightarrow \mathbb G$ where the composition operator $C_{\varphi } $ is a bounded operator $Hv(\mathbb G) \rightarrow Hv(\mathbb G)$ by a simple property which depends only on $\varphi $ but not on $v$. Moreover we show that there are no compact composition operators $C_{\varphi }$ on $Hv(\mathbb G)$.

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