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Carleson measures and Toeplitz operators on small Bergman spaces on the ball

Van An Le — 2021

Czechoslovak Mathematical Journal

We study Carleson measures and Toeplitz operators on the class of so-called small weighted Bergman spaces, introduced recently by Seip. A characterization of Carleson measures is obtained which extends Seip’s results from the unit disk of to the unit ball of n . We use this characterization to give necessary and sufficient conditions for the boundedness and compactness of Toeplitz operators. Finally, we study the Schatten p classes membership of Toeplitz operators for 1 < p < .

Convex quadratic underestimation and Branch and Bound for univariate global optimization with one nonconvex constraint

Hoai An Le ThiMohand Ouanes — 2006

RAIRO - Operations Research

The purpose of this paper is to demonstrate that, for globally minimize one dimensional nonconvex problems with both twice differentiable function and constraint, we can propose an efficient algorithm based on Branch and Bound techniques. The method is first displayed in the simple case with an interval constraint. The extension is displayed afterwards to the general case with an additional nonconvex twice differentiable constraint. A quadratic bounding function which is better than the well known...

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