Hankel operators on holomorphic Hardy-Orlicz spaces

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Carleson measures for Hardy Sobolev spaces and Generalized Bergman spaces

Carleson measures for various spaces of holomorphic functions in the unit ball have been studied extensively since Carleson’s original result for the disk. In the first paper of this thesis, we give, by means of Green’s formula, an alternative proof of the characterization of Carleson measures for some Hardy Sobolev spaces (including Hardy space) in the unit ball. In the second paper of this thesis, we give a new characterization of Carleson measures for the Generalized Bergman spaces on the unit ball using singular integral techniques

Carleson measures for the generalized Bergman spaces via a T(1)-type theorem

In this paper, we give a new characterization of Carleson measures for the generalized Bergman spaces. We show first that this problem is equivalent to a T(1)-type problem. Using an idea of Verdera (see [V]), we introduce a sort of curvature in the unit ball adapted to our kernel. We establish a good lambda inequality which then yields the solution of this T(1)-type problem

Hankel operators on holomorphic Hardy-Orlicz spaces

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On Hankel Forms of Higher Weights: The Case of Hardy Spaces

In this paper we study bilinear Hankel forms of higher weights on Hardy spaces in several dimensions. (The Schatten class Hankel forms of higher weights on weighted Bergman spaces have already been studied by Janson and Peetre for one dimension and by Sundhall for several dimensions). We get a full characterization of Schatten class Hankel forms in terms of conditions for the symbols to be in certain Besov spaces. Also, the Hankel forms are bounded and compact if and only if the symbols satisfy certain Carleson measure criteria and vanishing Carleson measure criteria, respectively

Hankel Operators with Weighted Lipschitz Symbols in the Unit Ball

We characterize symbols of bounded Hankel operators between some Hardy-Orlicz spaces and usual Hardy spaces in the unit ball of $\mathbf{C}^n$