Bernstein–Walsh-Type Polynomial Inequalities in Domains Bounded by Piecewise Asymptotically Conformal Curve with Nonzero Inner Angles in the Bergman Space

2019 ◽  
Vol 71 (5) ◽  
pp. 663-676
Author(s):  
F. G. Abdullayev ◽  
G. A. Abdullayev ◽  
D. Şimşek
Keyword(s):  
Bergman Space ◽  
Polynomial Inequalities ◽  
Asymptotically Conformal Curve

scholarly journals Polynomial Inequalities in Regions with Piecewise Asymptotically Conformal Curve in the Weighted Lebesgue Space

2018 ◽  
Vol 3 (2) ◽  
pp. 100-112
Author(s):  
F.G. ABDULLAYEV ◽  
◽  
D. SIMSEK ◽  
N. SAYPIDINOVA ◽  
Z. TASHPAEVA ◽  
...  
Keyword(s):  
Lebesgue Space ◽  
Weighted Lebesgue Space ◽  
Polynomial Inequalities ◽  
Asymptotically Conformal Curve

Polynomial Inequalities in Regions with Zero Interior Angles in the Bergman Space

2018 ◽  
Vol 70 (3) ◽  
pp. 362-384
Author(s):  
S. Balci ◽  
M. Imash-kyzy ◽  
F. G. Abdullayev
Keyword(s):  
Bergman Space ◽  
Polynomial Inequalities

scholarly journals Compact Differences of Composition Operators on Bergman Spaces Induced by Doubling Weights

2021 ◽  
Author(s):  
Bin Liu ◽  
Jouni Rättyä ◽  
Fanglei Wu
Keyword(s):  
Bergman Space ◽  
Open Problem ◽  
Lebesgue Space ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Carleson Measures ◽  
Doubling Weights ◽  
The Way

AbstractBounded and compact differences of two composition operators acting from the weighted Bergman space $$A^p_\omega $$ A ω p to the Lebesgue space $$L^q_\nu $$ L ν q , where $$0<q<p<\infty $$ 0 < q < p < ∞ and $$\omega $$ ω belongs to the class "Equation missing" of radial weights satisfying two-sided doubling conditions, are characterized. On the way to the proofs a new description of q-Carleson measures for $$A^p_\omega $$ A ω p , with $$p>q$$ p > q and "Equation missing", involving 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. The case "Equation missing" is also briefly discussed and an open problem concerning this case is posed.

scholarly journals Hyponormality of Toeplitz operators with non-harmonic symbols on the Bergman spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sumin Kim ◽  
Jongrak Lee
Keyword(s):  
Toeplitz Operator ◽  
Bergman Space ◽  
Toeplitz Operators ◽  
Bergman Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

AbstractIn this paper, we present some necessary and sufficient conditions for the hyponormality of Toeplitz operator $T_{\varphi }$ T φ on the Bergman space $A^{2}(\mathbb{D})$ A 2 ( D ) with non-harmonic symbols under certain assumptions.

scholarly journals The Berezin Transform of Toeplitz Operators on the Weighted Bergman Space

2021 ◽  
Author(s):  
Cezhong Tong ◽  
Junfeng Li ◽  
Hicham Arroussi
Keyword(s):  
Bergman Space ◽  
Toeplitz Operators ◽  
Reproducing Kernel ◽  
Bergman Spaces ◽  
Essential Norm ◽  
Berezin Transform ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Kernel Estimates ◽  
Berezin Transforms

AbstractIn this paper, we obtain some interesting reproducing kernel estimates and some Carleson properties that play an important role. We characterize the bounded and compact Toeplitz operators on the weighted Bergman spaces with Békollé-Bonami weights in terms of Berezin transforms. Moreover, we estimate the essential norm of them assuming that they are bounded.

scholarly journals Polynomial inequalities on the Hamming cube

2020 ◽  
Vol 178 (1-2) ◽  
pp. 235-287
Author(s):  
Alexandros Eskenazis ◽  
Paata Ivanisvili
Keyword(s):  
Polynomial Inequalities

scholarly journals Toeplitz Operators on the Bergman Space of Planar Domains with Essentially Radial Symbols

2011 ◽  
Vol 2011 ◽  
pp. 1-26 ◽  
Author(s):  
Roberto C. Raimondo
Keyword(s):  
Bergman Space ◽  
Toeplitz Operators ◽  
Boundary Behavior ◽  
Berezin Transform ◽  
Planar Domain ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Planar Domains ◽  
Necessary And Sufficient ◽  
The Relationship

We study the problem of the boundedness and compactness of when and is a planar domain. We find a necessary and sufficient condition while imposing a condition that generalizes the notion of radial symbol on the disk. We also analyze the relationship between the boundary behavior of the Berezin transform and the compactness of

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