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Projections on Hardy spaces in the Lie ball.

David Bekollé — 1994

Publicacions Matemàtiques

On the Lie ball w of C, n ≥ 3, we prove that for all p ∈ [1,∞), p ≠ 2, the Hardy space H(w) is an uncomplemented subspace of the Lebesgue space L(∂w, dσ), where ∂w denotes the Shilov boundary of w and dσ is a normalized invariant measure of ∂w.

Reproducing properties and L p -estimates for Bergman projections in Siegel domains of type II

David BékolléAnatole Temgoua Kagou — 1995

Studia Mathematica

On homogeneous Siegel domains of type II, we prove that under certain conditions, the subspace of a weighted L p -space (0 < p < ∞) consisting of holomorphic functions is reproduced by a weighted Bergman kernel. We also obtain some L p -estimates for weighted Bergman projections. The proofs rely on a generalization of the Plancherel-Gindikin formula for the Bergman space A 2 .

Nonautonomous partial functional differential equations; existence and regularity

Moussa El-Khalil KpoumièKhalil EzzinbiDavid Békollè — 2017

Nonautonomous Dynamical Systems

The aim of this work is to establish several results on the existence and regularity of solutions for some nondensely nonautonomous partial functional differential equations with finite delay in a Banach space. We assume that the linear part is not necessarily densely defined and generates an evolution family under the conditions introduced by N. Tanaka.We show the local existence of the mild solutions which may blow up at the finite time. Secondly,we give sufficient conditions ensuring the existence...

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