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Semi-norms of the Bergman projection [PDF]

Computational Methods and Function Theory, 2015
It is known that the Bergman projection operator maps the space of essentially bounded functions in the unit ball in the d-dimensional complex vector space onto the Bloch space of the unit ball. This paper deals with the various semi-norms of the Bergman
Markovic, Marijan
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Solution of Extremal Problems in Bergman Spaces Using the Bergman Projection [PDF]

Computational Methods and Function Theory, 2013
In this paper we discuss the explicit solution of certain extremal problems in Bergman spaces. In order to do this, we develop methods to calculate the Bergman projections of various functions.
Ferguson, Timothy
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Norm of the Bergman projection [PDF]

MATHEMATICA SCANDINAVICA, 2012
This paper deals with the the norm of the weighted Bergman projection operator $P_\alpha:L^\infty\to \mathcal{B}$ where $\alpha>-1$ and $\mathcal{B}$ is the Bloch space of the unit ball of the complex space $\mathbf{C}^n$.
Kalaj, David, Markovic, Marijan
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Weighted Bergman Projection on the Hartogs Triangle [PDF]

Journal of Mathematical Analysis and Applications, 2015
We prove the $L^p$ regularity of the weighted Bergman projection on the Hartogs triangle, where the weights are powers of the distance to the singularity at the boundary. The restricted range of $p$ is proved to be sharp. By using a two-weight inequality
Chen, Liwei
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Bergman Projection on the Symmetrized Bidisk

The Journal of Geometric Analysis, 2023
We apply the Bekollé-Bonami estimate for the (positive) Bergman projection on the weighted $L^p$ spaces on the unit disk. As the consequences, we obtain the boundedness of the Bergman projection on the weighted Sobolev space on the symmetrized bidisk. We also improve the boundedness result of the Bergman projection on the unweighted $L^p$ space on the ...
Liwei Chen, Muzhi Jin, Yuan Yuan
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Sharp Bekolle estimates for the Bergman projection

Journal of Functional Analysis, 2012
We prove sharp estimates for the Bergman projection in weighted Bergman spaces in terms of the Bekolle constant. Our main tools are a dyadic model dominating the operator and an adaptation of a method of Cruz-Uribe, Martell and Perez.Comment: 12 pages, 1
Pott, Sandra, Reguera, Maria Carmen
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Bergman projection induced by radial weight [PDF]

Advances in Mathematics, 2021
The question of when the Bergman projection $P_ω$ induced by a radial weight $ω$ on the unit disc is a bounded operator from one space into another is of primordial importance in the theory of Bergman spaces. The long-standing problem of describing the radial weights $ω$ such that $P_ω$ is bounded on the Lebesgue space $L^p_ω$ had been known to experts
Rättyä, Jouni, Peláez-Márquez, José Ángel   +1 more
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Bergman spaces with exponential type weights

Journal of Inequalities and Applications, 2021
For 1 ≤ p < ∞ $1\le ...
Hicham Arroussi
doaj   +1 more source

Sobolev Estimates for the $\overline{\partial }$ and the $\overline{\partial }$-Neumann Operator on Pseudoconvex Manifolds

Mathematics, 2023
Let D be a relatively compact domain in an n-dimensional Kähler manifold with a C2 smooth boundary that satisfies some “Hartogs-pseudoconvexity” condition.
Haroun Doud Soliman Adam, Khalid Ibrahim Adam Ahmed, Sayed Saber, Marin Marin   +3 more
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Reproducing Kernels for Hardy and Bergman Spaces of the Upper Half Plane

Communications in Advanced Mathematical Sciences, 2020
Using invertible isometries between Hardy and Bergman spaces of the unit disk $\D$ and the corresponding spaces of the upper half plane $\uP$, we determine explicitly the reproducing kernels for the Hardy and Bergman spaces of $\uP$. As a consequence, we
Job Bonyo
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