Papers by Jocelyn Gonessa
arXiv (Cornell University), Mar 22, 2017
Starting from an adapted Whitney decomposition of tube domains in C n over irreducible symmetric ... more Starting from an adapted Whitney decomposition of tube domains in C n over irreducible symmetric cones of R n , we prove an atomic decomposition theorem in mixed norm weighted Bergman spaces on these domains. We also characterize the interpolation space via the complex method between two mixed norm weighted Bergman spaces.
arXiv (Cornell University), Mar 22, 2017
We present a transference principle of Lebesgue mixed norm estimates for Bergman projectors from ... more We present a transference principle of Lebesgue mixed norm estimates for Bergman projectors from tube domains over homogeneous cones to homogeneous Siegel domains of type II associated to the same cones. This principle implies improvements of these estimates for homogeneous Siegel domains of type II associated with Lorentz cones, e.g. the Pyateckii-Shapiro Siegel domain of type II.
Multilinear Schur-type tests and boundedness of multilinear Bergman-type operators
Monatshefte für Mathematik, Mar 23, 2023
Complex Interpolation Between Two Mixed Norm Bergman Spaces in Tube Domains Over Homogeneous Cones
Complex Analysis and Operator Theory
Multilinear Schur-type tests and boundedness of multilinear Bergman-type operators
Monatshefte für Mathematik, Mar 23, 2023
Sharp Norm Estimates for Weighted Bergman Projections in the Mixed Norm Spaces
Journal of Contemporary Mathematical Analysis, Nov 1, 2018
In this paper, we show that the norm of the Bergman projection on Lp,q-spaces in the upper half-p... more In this paper, we show that the norm of the Bergman projection on Lp,q-spaces in the upper half-plane is comparable to csc(π/q). Then we extend this result to a more general class of domains, known as the homogeneous Siegel domains of type II.
Cornell University - arXiv, Oct 28, 2020
Very recently, E. H. Lieb and J. P. Solovej stated a conjecture about the constant of embedding b... more Very recently, E. H. Lieb and J. P. Solovej stated a conjecture about the constant of embedding between two Bergman spaces of the upper-half plane. A question in relation with a Werhltype entropy inequality for the affine AX + B group. More precisely, that for any holomorphic function F on the upper-half plane Π + , Π + |F (x+iy)| 2s y 2s−2 dxdy ≤ π 1−s (2s − 1)2 2s−2 Π + |F (x + iy)| 2 dxdy s for s ≥ 1, and the constant π 1−s (2s−1)2 2s−2 is sharp. We prove differently that the above holds whenever s is an integer and we prove that it holds when s → ∞. We also prove that when restricted to powers of the Bergman kernel, the conjecture holds. We next study the case where s is close to 1. Hereafter, we transfer the conjecture to the unit disc where we show that the conjecture holds when restricted to analytic monomials. Finally, we overview the bounds we obtain in our attempts to prove the conjecture.
arXiv: Complex Variables, Oct 28, 2020
Very recently, E. H. Lieb and J. P. Solovej stated a conjecture about the constant of embedding b... more Very recently, E. H. Lieb and J. P. Solovej stated a conjecture about the constant of embedding between two Bergman spaces of the upper-half plane. A question in relation with a Werhltype entropy inequality for the affine AX + B group. More precisely, that for any holomorphic function F on the upper-half plane Π + , Π + |F (x+iy)| 2s y 2s−2 dxdy ≤ π 1−s (2s − 1)2 2s−2 Π + |F (x + iy)| 2 dxdy s for s ≥ 1, and the constant π 1−s (2s−1)2 2s−2 is sharp. We prove differently that the above holds whenever s is an integer and we prove that it holds when s → ∞. We also prove that when restricted to powers of the Bergman kernel, the conjecture holds. We next study the case where s is close to 1. Hereafter, we transfer the conjecture to the unit disc where we show that the conjecture holds when restricted to analytic monomials. Finally, we overview the bounds we obtain in our attempts to prove the conjecture.
arXiv: Complex Variables, 2017
We characterise functions for the dual spaces of entire functions f such that fe^{-\phi}\in L^p(\... more We characterise functions for the dual spaces of entire functions f such that fe^{-\phi}\in L^p(\C^n,\rho^{-2}dA), 0<p\leq 1, where \phi is a subharmonic weight and \rho^{-2} is a positive function called under certain conditions regularised version of Laplacian \Delta\phi, as described in \cite{C}.
Mathematische Annalen, 2018
We present a transference principle of Lebesgue mixed norm estimates for Bergman projectors from ... more We present a transference principle of Lebesgue mixed norm estimates for Bergman projectors from tube domains over homogeneous cones to homogeneous Siegel domains of type II associated to the same cones. This principle implies improvements of these estimates for homogeneous Siegel domains of type II associated with Lorentz cones, e.g. the Pyateckii-Shapiro Siegel domain of type II.
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2020
Starting from an adapted Whitney decomposition of tube domains in C n over irreducible symmetric ... more Starting from an adapted Whitney decomposition of tube domains in C n over irreducible symmetric cones of R n , we prove an atomic decomposition theorem in mixed norm weighted Bergman spaces on these domains. We also characterize the interpolation space via the complex method between two mixed norm weighted Bergman spaces.
Toeplitz products on the vector weighted Bergman spaces
Acta Scientiarum Mathematicarum, 2014
Comptes Rendus Mathematique, 2003
We prove that the complex interpolation space [A p 0 ν , A p 1 ν ] θ , 0 < θ < 1, between two wei... more We prove that the complex interpolation space [A p 0 ν , A p 1 ν ] θ , 0 < θ < 1, between two weighted Bergman spaces A p 0 ν and A p 1 ν on the tube in C n , n 3, over an irreducible symmetric cone of R n is the weighted Bergman space A p ν with 1/p = (1 − θ)/p 0 + θ/p 1. Here, ν > n/r − 1 and 1 p 0 < p 1 < 2 + ν/(n/r − 1) where r denotes the rank of the cone. We then construct an analytic family of operators and an atomic decomposition of functions, which are related to this interpolation result. To cite this article: D.
Archiv der Mathematik, 2013
In this note we prove a duality theorem for generalized Fock spaces.
Annales Polonici Mathematici, 2012
We establish L p-estimates for the weighted Bergman projection on a nonsingular cone. We apply th... more We establish L p-estimates for the weighted Bergman projection on a nonsingular cone. We apply these results to the weighted Fock space with respect to the minimal norm in C n .
arXiv: Complex Variables, 2019
We study the $L^p-L^q$ boundedness of Bergman projector on the minimal ball. This improves an imp... more We study the $L^p-L^q$ boundedness of Bergman projector on the minimal ball. This improves an important result of \cite{MY} due to G. Mengotti and E. H. Youssfi.
New York Journal of Mathematics, 2011
We show that, for 1 < p < ∞, the norm of the weighted Bergman projection P s,B * on L p (B * , |z... more We show that, for 1 < p < ∞, the norm of the weighted Bergman projection P s,B * on L p (B * , |z • z| p−2 2 dvs) is comparable to csc(π/p), where B * is the minimal unit ball in C n .
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Papers by Jocelyn Gonessa