arXiv subjects

Edgar Tchoundja

Publications and source records attributed to Edgar Tchoundja.

4 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↗

arXiv2016

Weighted Estimates for the Berezin Transform and Bergman Projection on the Unit Ball in $\mathbb{C}^{n}$

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 in $\mathbb{C}^n$. The estimates are in terms of the Bekolle-Bonami constant of the weight.

math.CA↗

arXiv2015

Duality for large Bergman-Orlicz spaces and Boundedness of Hankel Operators

For $\mathbb B^n$ the unit ball of $\mathbb C^n$, we consider Bergman-Orlicz spaces of holomorphic functions in $L^Φ_α$, which are generalizations of classical Bergman spaces. We characterize the dual space of large Bergman-Orlicz space, and bounded Hankel operators between some Bergman-Orlicz spaces $A_α^{Φ_1}(\mathbb B^n)$ and $A_α^{Φ_2}(\mathbb B^n)$ where $Φ_1$ and $Φ_2$ are either convex or concave growth functions.

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arXiv2012

Hankel operators on holomorphic Hardy-Orlicz spaces

We characterize the symbols of Hankel operators that ex- tend into bounded operators from the Hardy-Orlicz $H^{Φ_1} (\mathbb B^n)$ into $H^{Φ_2} (\mathbb B^n)$ in the unit ball of Cn, in the case where the growth functions $?Φ_1$ and $Φ_2$ are either concave or convex. The case where the growth functions are both concave has been studied by Bonami and Sehba. We also obtain several weak factorization theorems for functions in $H^Φ(\mathbb B^n)$, with concave growth function, in terms of products of Hardy-Orlicz functions with convex growth functions.

math.CA↗