arXiv subjects

David Bekolle

Publications and source records attributed to David Bekolle.

5 recordsLinked to original sources

arXiv2018

Atomic decomposition and Weak Factorization for Bergman-Orlicz spaces

For $\mathbb B^n$ the unit ball of $\mathbb C^n$, we consider Bergman-Orlicz spaces of holomorphic functions in $L^Φ_α(\mathbb B^n)$, which are generalizations of classical Bergman spaces. We obtain atomic decomposition for functions in the Bergman-Orlicz space $\mathcal A^Φ_α(\mathbb B^n)$ where $Φ$ is either convex or concave growth function. We then prove weak factorization theorems involving the Bloch space and a Bergman-Orlicz space and also weak factorization theorems involving two Bergman-Orlicz spaces.

math.CA↗

arXiv2017

Lebesgue mixed norm estimates for Bergman projectors: from tube domains over homogeneous cones to homogeneous Siegel domains of type II

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.

math.CA↗

arXiv2017

Bergman-Lorentz spaces on tube domains over symmetric cones

We study Bergman-Lorentz spaces on tube domains over symmetric cones, i.e. spaces of holomorphic functions which belong to Lorentz spaces $L(p, q).$ We establish boundedness and surjectivity of Bergman projectors from Lorentz spaces to the corresponding Bergman-Lorentz spaces and real interpolation between Bergman-Lorentz spaces. Finally we ask a question whose positive answer would enlarge the interval of parameters $p\in (1, \infty)$ such that the relevant Bergman projector is bounded on $L^p$ for cones of rank $r\geq 3.$

math.CA↗

arXiv2017

Atomic decomposition and interpolation via the complex method for mixed norm Bergman spaces on tube domains over symmetric cones

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.

math.CA↗

arXiv2015

Nonlinear Luenberger-like observers for some anthracnose models

In this paper, we propose observers for the dynamics of anthracnose disease described in [12]. Spatial and non spatial versions of the observers are given following an approach similar to [12]. The models given in [12] are improved in order to be more realistic. The conditions on parameters are more general. There are also changes in the equations modelling the dynamics of the berry volume (v) and the rot volume (v_r). We study theoretically the proposed observers in terms of well-posedness and convergence. We make several simulations to assess the effectiveness of observers which definitely display fairly good behaviour.

math.OC↗