Cauchy-Fantappie Type Operators And Duality On Poletsky-Stessin Hardy Spaces of Complex Ellipsoids

Abstract

In the first part of this study we consider the boundedness and compactness properties of Cauchy-Fantappie type operators on Poletsky-Stessin Hardy spaces $H_u^p({\mathbb{B}}^{\text{p}})$ of complex ellipsoids. We show that boundedness and compactness criteria are given by the Carleson conditions. In addition we give a basic compactness property for the subsets of $H_u^p({\mathbb{B}}^{\text{p}})$ spaces and the characterization of weakly convergent sequences in $H_u^p({\mathbb{B}}^{\text{p}})$. In the second part we will discuss the dual complement of the complex ellipsoid and we will give a duality result for $H_u^p({\mathbb{B}}^{\text{p}})$ spaces in the sense of Grothendieck-Köthe-da Silva.

arXiv commentThis paper has been withdrawn by the author since it is going to be changed considerably

References in corpus (1)

• Poletsky-Stessin Hardy Spaces on Complex Ellipsoids in C^n