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.

scholarly journals Compact differences of weighted composition operators

2020 ◽  
Author(s):  
Bin Liu ◽  
Jouni Rättyä
Keyword(s):  
Bergman Space ◽  
Composition Operators ◽  
Weighted Bergman Space ◽  
Carleson Measures ◽  
Weighted Composition Operators ◽  
Doubling Weights ◽  
Weighted Composition ◽  
The Way

AbstractCompact differences of two weighted composition operators acting from the weighted Bergman space $$A^p_{\omega }$$ A ω p to another weighted Bergman space $$A^q_{\nu }$$ A ν q , where $$0<p\le q<\infty $$ 0 < p ≤ q < ∞ and $$\omega ,\nu $$ ω , ν belong to the class $${\mathcal {D}}$$ D of radial weights satisfying two-sided doubling conditions, are characterized. On the way to the proof a new description of q-Carleson measures for $$A^p_{\omega }$$ A ω p , with $$\omega \in {\mathcal {D}}$$ ω ∈ D , in terms of pseudohyperbolic discs is established. This last-mentioned result generalizes the well-known characterization of q-Carleson measures for the classical weighted Bergman space $$A^p_{\alpha }$$ A α p with $$-1<\alpha <\infty $$ - 1 < α < ∞ to the setting of doubling weights.

scholarly journals Invertible Weighted Composition Operators on the Fock Space ofCN

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Liankuo Zhao
Keyword(s):  
Fock Space ◽  
Composition Operators ◽  
Complete Characterization ◽  
Weighted Composition Operators ◽  
Weighted Composition

We give a complete characterization of bounded invertible weighted composition operators on the Fock space ofCN.

scholarly journals Weighted composition operators on functional Hilbert spaces

1985 ◽  
Vol 31 (1) ◽  
pp. 117-126 ◽  
Author(s):  
R.K. Singh ◽  
R. David Chandra Kumar
Keyword(s):  
Hilbert Spaces ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Linear Operators ◽  
Weighted Composition Operators ◽  
Bounded Linear ◽  
Atomic Measure ◽  
Weighted Composition ◽  
Functional Hilbert Spaces

Let X be a non-empty set and let H(X) denote a Hibert space of complex-valued functions on X. Let T be a mapping from X to X and θ a mapping from X to C such that for all f in H(X), f ° T is in H(x) and the mappings CT taking f to f ° T and M taking f to θ.f are bounded linear operators on H(X). Then the operator CTMθ is called a weighted composition operator on H(X). This note is a report on the characterization of weighted composition operators on functional Hilbert spaces and the computation of the adjoint of such operators on L2 of an atomic measure space. Also the Fredholm criteria are discussed for such classes of operators.

scholarly journals WEIGHTED COMPOSITION OPERATORS AND DYNAMICAL SYSTEMS

1998 ◽  
Vol 29 (2) ◽  
pp. 101-107
Author(s):  
R. K. SINGH ◽  
BHOPINDER SINGH
Keyword(s):  
Hausdorff Space ◽  
Weighted Space ◽  
Composition Operators ◽  
Continuous Functions ◽  
Weighted Composition Operators ◽  
Linear Dynamical System ◽  
Completely Regular ◽  
Weighted Composition ◽  
Locally Convex

Let $X$ be a completely regular Hausdorff space, $E$ a Hausdorff locally convex topo­logical vector space, and $V$ a system of weights on $X$. Denote by $CV_b(X, E)$ ($CV_o(X, E)$) the weighted space of all continuous functions $f : X \to E$ such that $vf (X)$ is bounded in $E$ (respectively, $vf$ vanishes at infinity on $X$) for all $v \in V$. In this paper, we give an improved characterization of weighted composition operators on $CV_b(X, E)$ and present a linear dynamical system induced by composition operators on the metrizable weighted space $CV_o(\mathbb{R}, E)$.

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