On Carleson measures and Hankel forms of higher weights on Hardy space - Tchoundja, Edgar
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In this book, we are concerned with two problems. The first problem is to describe Carleson measures for Hardy Sobolev spaces and the generalized Bergman spaces in the unit ball. 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). We also give a new characterization of Carleson measures for the generalized Bergman spaces (including the Drury-Averson space) on the unit ball, in terms of testing on balls, using T(1)-Theorem type techniques for singular integrals. The second problem concerns…mehr

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Produktbeschreibung
In this book, we are concerned with two problems. The first problem is to describe Carleson measures for Hardy Sobolev spaces and the generalized Bergman spaces in the unit ball. 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). We also give a new characterization of Carleson measures for the generalized Bergman spaces (including the Drury-Averson space) on the unit ball, in terms of testing on balls, using T(1)-Theorem type techniques for singular integrals. The second problem concerns bilinear Hankel forms of higher weights on Hardy spaces of the unit ball. We show that these Hankel forms are bounded and compact if and only if the symbols satisfy certain Carleson measure criteria and vanishing Carleson measure criteria, respectively. We get a full characterization of Schatten class Sp Hankel forms for p great or equal to 2, in terms of the membership for the symbols to be in certain Besov spaces.
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Autorenporträt
Dr. Edgar Tchoundja is currently Senior Lecturer at the department of Mathematics at the University of Yaounde I in Cameroon. He completed his Ph.D. from the same University in 2009. His research area is Analysis and His research interests include Function and Operator Theory in Several Variables, Harmonic Analysis and Complex Analysis.