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Projective generators inHardy and Bergman spaces
Bulletin des Sciences Mathématiques, 2000 A function \(f\) in the Bergman space \(A^2\) (respectively, the Hardy space \(H^2)\) is called a projective generator of defect \(n\) if \[ \text{codim}_{[g]} [P_{[g]}f]\leq n \] for any \(g\in A^2\) (respectively, \(H^2)\) such that \(P_{[g]}f\neq 0\), and if equality holds for some \(g\).
Korenblum, B. +2 more
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L∞-Estimates of the Bergman projection in the Lie ball of ℂn
Journal of Function Spaces and Applications, 2011 In this paper, we consider estimates with loss for the Bergman projections of bounded symmetric domains of ℂn in their Harish-Chandra realizations. This paper is twofold: on one side we develop transfer methods between these bounded domains and their ...
Cyrille Nana
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A Sharp Constant for the Bergman Projection [PDF]
Canadian Mathematical Bulletin, 2015 AbstractFor the Bergman projection operator P we prove thatHere λ stands for the hyperbolic metric in the unit ball B of Cn, and B1 denotes the Besov space with an adequate semi-norm. We also consider a generalization of this result. This generalizes some recent results due to Perälä.
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On estimates for weighted Bergman projections [PDF]
Proceedings of the American Mathematical Society, 2015 In this note we show that the weighted $L^{2}$-Sobolev estimates obtained by P. Charpentier, Y. Dupain & M. Mounkaila for the weighted Bergman projection of the Hilbert space $L^{2}\left( ,d _{0}\right)$ where $ $ is a smoothly bounded pseudoconvex domain of finite type in $\mathbb{C}^{n}$ and $ _{0}=\left(- _{0}\right)^{r}d $, $ $ being the
Charpentier, P. +2 more
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Derivatives of the Berezin Transform
Journal of Function Spaces and Applications, 2012 For a rotation invariant domain Ω, we consider A2(Ω,μ) the Bergman space and we investigate some properties of the rank one projection A(z):=〈⋅,kz〉kz. We prove that the trace of all the strong derivatives of A(z) is zero. We also focus on the generalized
Hélène Bommier-Hato
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Harmonic Analysis Techniques in Several Complex Variables
Bruno Pini Mathematical Analysis Seminar, 2014 We give a survey of recent joint work with E.M. Stein (Princeton University) concerning the application of suitable versions of the T(1)-theorem technique to the study of orthogonal projections onto the Hardy and Bergman spaces of holomorphic functions ...
Loredana Lanzani
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Bergman subspaces and subkernels: Degenerate $L^p$ mapping and zeroes
, 2017 Regularity and irregularity of the Bergman projection on $L^p$ spaces is established on a natural family of bounded, pseudoconvex domains. The family is parameterized by a real variable $\gamma$. A surprising consequence of the analysis is that, whenever
Edholm, L. D., McNeal, J. D.
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Bergman Projection on Lebesgue Space Induced by Doubling Weight
Results in Mathematics, 2023 AbstractLet $$\omega $$ ω and $$\nu $$ ν be radial weights on the unit disc of the complex plane, and denote $$\sigma =\omega ^{p'} \nu ^{-\frac{p'}{p}}$$ σ = ω
José Ángel Peláez +2 more
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Sharp Weighted Bounds for Multilinear Fractional Type Operators Associated with Bergman Projection
Journal of Function Spaces, 2018 We first introduce the multiple weights which are suitable for the study of Bergman type operators. Then, we give the sharp weighted estimates for multilinear fractional Bergman operators and fractional maximal function.
Juan Zhang, Senhua Lan, Qingying Xue
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ON SOME NEW PROJECTION THEOREMS AND SHARP ESTIMATES IN HERZ TYPE SPACES IN BOUNDED PSEUDOCONVEX DOMAINS [PDF]
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2018 We prove new projection theorems for new Herz type spaces in various domains in Cn in the unit disk, unit ball, bounded pseudoconvex domains and based on these results we provide sharp estimates for distances in such type spaces under one condition on ...
R. F. Shamoyan, A. N. Shipka
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