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Weighted estimates for the Berezin transform and Bergman projection on the unit ball

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1 Published in 2017 at "Mathematische Zeitschrift"

DOI: 10.1007/s00209-016-1809-4

Abstract: Using modern techniques of dyadic harmonic analysis, we are able to prove sharp estimates for the Bergman projection and Berezin transform and more general operators in weighted Bergman spaces on the unit ball. The estimates… read more here.

Keywords: berezin transform; bergman projection; unit ball;

m-Berezin Transform and Approximation of Operators on the Bergman Space Over Bounded Symmetric Domains

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1 Published in 2017 at "Complex Analysis and Operator Theory"

DOI: 10.1007/s11785-015-0519-y

Abstract: We study m-Berezin transforms of bounded operators on the Bergman space over a bounded symmetric domain, $$\Omega $$Ω. We use the m-Berezin transform to establish some results on norm approximation of bounded linear operators acting… read more here.

Keywords: berezin transform; operators bergman; bounded symmetric; bergman space ... See more keywords

Closed Range Type Properties of Toeplitz Operators on the Bergman Space and the Berezin Transform

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1 Published in 2019 at "Complex Analysis and Operator Theory"

DOI: 10.1007/s11785-019-00949-4

Abstract: We characterize the multiplication operators with closed range on the Bergman space in terms of the Berezin transform, and apply this characterization to finite products of interpolating Blaschke products. We give some necessary and some… read more here.

Keywords: closed range; bergman space; toeplitz operators; berezin transform ... See more keywords

Berezin transform of slice functions

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1 Published in 2017 at "Complex Variables and Elliptic Equations"

DOI: 10.1080/17476933.2016.1250398

Abstract: In a recent paper, we introduced the Berezin transform of quaternionic linear operators and we obtained some properties in the setting of weighted Bergman spaces of slice hyperholomorphic functions. Here, we define the Berezin transform… read more here.

Keywords: berezin transform; transform slice; slice functions;

Berezin transform and Toeplitz operators on polygonal domains

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0 Published in 2021 at "Complex Variables and Elliptic Equations"

DOI: 10.1080/17476933.2021.1978437

Abstract: We consider reflexive Bergman spaces on polygonal domains Ω of the complex plane. With some restrictions to the angles of the boundary of Ω, we show that the boundedness of the Toeplitz operator with a… read more here.

Keywords: berezin transform; transform toeplitz; toeplitz operators; polygonal domains ... See more keywords

A sufficient condition for Lp regularity of the Berezin transform

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2 Published in 2022 at "Complex Variables and Elliptic Equations"

DOI: 10.1080/17476933.2022.2052864

Abstract: KΩ(z, z) is the normalized Bergman kernel as ‖kz ‖L2 = 1 for all z ∈ Ω where ‖.‖Lp denotes the Lp norm on Ω. Next we will define the Berezin transform of a bounded… read more here.

Keywords: berezin transform; operator; regularity berezin; transform ... See more keywords