Yusuf Abu Muhanna, El-Bachir Yallaoui, "Absolutely continuous measures and compact composition operator on spaces of Cauchy transforms", International Journal of Mathematics and Mathematical Sciences, vol. 2004, Article ID 321430, 9 pages, 2004. https://doi.org/10.1155/S0161171204310057
Absolutely continuous measures and compact composition operator on spaces of Cauchy transforms
The analytic self-map of the unit disk , is said to induce a composition operator from the Banach space to the Banach space if for all . For and , the families of weighted Cauchy transforms are defined by , where is complex Borel measure, belongs to the unit circle , and the kernel . In this paper, we will explore the relationship between the compactness of the composition operator acting on and the complex Borel measures .
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