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Concrete Operators, ISSN 2299-3282, 08/2019, Volume 6, Issue 1, pp. 76 - 81
We characterize closed range composition operators on the Dirichlet space for a particular class of composition symbols. The characterization relies on a... 
composition operator | 30H35 | Dirichlet space | Berezin transform | 47B33 | 30J10 | Toeplitz operator | 47A53 | vanishing mean oscillation | 30H25 | closed range operator | dirichlet space | toeplitz operator | 47b33 | 30h25 | 30j10 | 47a53 | 30h35 | berezin transform
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2018, Volume 461, Issue 1, pp. 657 - 675
We characterize the isometric weighted composition operators on weighted Bergman spaces over the unit disk. We also determine the Wold decomposition of... 
Weighted Bergman spaces | Isometry | Numerical range | Weighted composition operators | Wold decomposition | MATHEMATICS | MATHEMATICS, APPLIED | HARDY
Journal Article
Complex Analysis and Operator Theory, ISSN 1661-8254, 11/2019, Volume 13, Issue 8, pp. 4027 - 4044
We characterize the multiplication operators with closed range on the Bergman space in terms of the Berezin transform, and apply this characterization to... 
Bergman space | Invertible operator | Closed range operator | Fredholm operator | 30H35 | 30J10 | Mathematics | Toeplitz operator | 47A53 | 30H20 | Operator Theory | Interpolating Blaschke product | Analysis | Multiplication operator | 47B35 | Mathematics, general | Berezin transform | MATHEMATICS | MATHEMATICS, APPLIED | HANKEL-OPERATORS
Journal Article
Integral Equations and Operator Theory, ISSN 0378-620X, 04/2017, Volume 87, Issue 4, pp. 581 - 600
We determine the boundedness and compactness of a large class of operators, mapping from general Banach spaces of holomorphic functions into a particular type... 
Banach spaces of holomorphic functions | Compactness | Growth spaces | Boundedness | Point evaluations | MATHEMATICS | WEIGHTED COMPOSITION OPERATORS | BANACH-SPACES | COMPACT COMPOSITION OPERATORS | ANALYTIC-FUNCTIONS | Mathematics - Functional Analysis
Journal Article
Computational Methods and Function Theory, ISSN 1617-9447, 6/2015, Volume 15, Issue 2, pp. 289 - 290
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2011, Volume 379, Issue 1, pp. 48 - 57
We study univalent functions f for which logf′ belongs to a class of general Besov-type spaces. We give a characterization of the general Besov-type domains in... 
Besov-type spaces | Carleson measures | Univalent functions | Schwarzian derivative | MATHEMATICS | VMOA | MATHEMATICS, APPLIED | HARMONIC MEASURE | BMOA | SPACES | UNIVALENT-FUNCTIONS
Journal Article
Complex Variables and Elliptic Equations, ISSN 1747-6933, 10/2015, Volume 60, Issue 10, pp. 1424 - 1430
We show that for , an analytic self-map of the unit disk with bounded weighted hyperbolic local distortion, the distortions boundedness from below on a... 
uniform local univalence | Bloch-type spaces | Primary: 30C45 | weighted hyperbolic distortion | 30F45 | Secondary: 30H30 | MATHEMATICS | BLOCH-SPACES | COMPOSITION OPERATORS | Distortion | Disks | Complex variables | Mathematical analysis | Images
Journal Article
International Journal of Mathematics and Mathematical Sciences, ISSN 0161-1712, 2011, Volume 2011, pp. 1 - 15
We present an overview of the known results describing the isometric and closed-range composition operators on different types of holomorphic function spaces.... 
Studies | Banach spaces | Function space | Mathematical analysis | Operators
Journal Article
Computational Methods and Function Theory, ISSN 1617-9447, 6/2015, Volume 15, Issue 2, pp. 277 - 287
We provide few results on the connections between the boundary regularity of an analytic self-map of the unit disk, and the boundary limits of its hyperbolic... 
Angular derivative | Computational Mathematics and Numerical Analysis | Functions of a Complex Variable | Hyperbolic distortion | 30H05 | Analysis | 30D40 | Boundary regularity | 30J10 | Mathematics | Finite Blaschke product | 30F45 | MATHEMATICS | MATHEMATICS, APPLIED | COMPOSITION OPERATORS | MAPS | SPACES | ANALYTIC-FUNCTIONS
Journal Article
Integral Equations and Operator Theory, ISSN 0378-620X, 4/2013, Volume 75, Issue 4, pp. 559 - 571
We characterize the Fredholm composition operators on the small Bloch-type spaces $${\mathcal{B}^{\alpha}}$$ , with 0 < α < 1, and give necessary and... 
sampling set | Fredholm operator | Analysis | Composition operators | Mathematics | Semi-Fredholm operator | Primary 47B35 | Bloch-type spaces | r-net | Secondary 32A18 | WEIGHTED COMPOSITION OPERATORS | COMPACT COMPOSITION OPERATORS | BOUNDEDNESS | ANALYTIC-FUNCTIONS | MATHEMATICS | HOLOMORPHIC-FUNCTIONS | CLOSED RANGE
Journal Article
Canadian Mathematical Bulletin, ISSN 0008-4395, 2012, Volume 55, Issue 2, pp. 441 - 448
While there is a large variety of univalently induced closed range composition operators on the Bloch space, we show that the only univalently induced, closed... 
Composition operators | Bloch-type spaces | Closed range | Univalent | closed range | MATHEMATICS | univalent | composition operators | SETS | BOUNDEDNESS | ANALYTIC-FUNCTIONS
Journal Article
International Journal of Mathematics and Mathematical Sciences, ISSN 0161-1712, 2003, Volume 2003, Issue 46, pp. 2929 - 2945
We prove that the boundedness and compactness of the Toeplitz operator on the Bergman space with aBMO1symbol is completely determined by the boundary behaviour... 
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 03/2003, Volume 131, Issue 3, pp. 793 - 800
We analyze the connection between compactness of operators on the Bergman space and the boundary behaviour of the corresponding Berezin transform. We prove... 
Topological compactness | Sufficient conditions | Hilbert spaces | Scalars | Mathematical functions | Mathematics | Counterexamples | Operator theory | Convergent boundaries | College mathematics | Berezin transform | Radial operator | Toeplitz operator | radial operator | MATHEMATICS | MATHEMATICS, APPLIED | TOEPLITZ-OPERATORS | BERGMAN SPACES
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2020, Volume 485, Issue 2, p. 123829
In this paper we prove that a Toeplitz operator with complex Borel measure symbol, whose total variation is Carleson, is weakly localized on the Bergman space.... 
Bergman space | Toeplitz operator | Carleson measure | Localization | [formula omitted] spaces | Toeplitz algebra | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRA | BMOp spaces | HANKEL-OPERATORS
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 05/2005, Volume 133, Issue 5, pp. 1371 - 1377
We give a necessary and sufficient condition for a composition operator C_{\phi } on the Bloch space to have closed range. We show that when \phi is univalent,... 
Line segments | Analytic functions | Mathematical functions | Mathematical inequalities | Abstracting | Range of function | College mathematics | MATHEMATICS | BERGMAN | MATHEMATICS, APPLIED
Journal Article
12/2015
We give a slight generalization of the characterization of finite Blaschke products given in a previous paper. The characterization uses the boundary behaviour... 
Mathematics - Complex Variables
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 12/2006, Volume 134, Issue 12, pp. 3531 - 3542
We characterize complex measures \mu on the unit disk for which the Toeplitz operator T_{\mu }^{\alpha }, \alpha >0, is bounded or compact on the Bloch type... 
Unit ball | Mathematical theorems | Analytic functions | Hankel operators | Mathematical functions | Necessary conditions | College mathematics | α-Bloch spaces | Toeplitz operators | MATHEMATICS | alpha-Bloch spaces | MATHEMATICS, APPLIED | HANKEL-OPERATORS
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 07/1998, Volume 126, Issue 7, pp. 2013 - 2023
We characterize bounded and compact composition operators on weighted Dirichlet spaces. The method involves integral averages of the determining function for... 
Circles | Tangents | Mathematical theorems | Analytic functions | Abstract spaces | Rectangles | Property composition | Mathematical functions | Necessary conditions | Composition operators | Dirichlet spaces | Angular derivatives | Carleson measures | MATHEMATICS | MATHEMATICS, APPLIED | composition operators | COMPACT COMPOSITION OPERATORS | angular derivatives
Journal Article
Integral Equations and Operator Theory, ISSN 0378-620X, 3/2008, Volume 60, Issue 3, pp. 435 - 449
We characterize complex measures μ on the unit disk for which the Toeplitz operator T μ is bounded or compact on the analytic Besov spaces B p with 1 ≤ p < ∞. 
analytic Besov spaces | Mathematics | Primary 47B35 | Toeplitz operators | Analysis | Secondary 32A18 | Analytic Besov spaces | MATHEMATICS | CARLESON MEASURES
Journal Article
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