Hardy Space Properties of the Cauchy Kernel Function for a Strictly Convex Planar Domain

<p>This work is based on a paper by Edgar Lee Stout, where it is shown that for every strictly pseudoconvex domain $D$ of class C² in \mathbb{C}^N, the Henkin-Ram\'irez Kernel Function belongs to the Smirnov class, E^q(D), for every $q\in(0,N)$.</p> <p>The main objective of this dissertation is to show an analogous result for the Cauchy Kernel Function and for any strictly convex bounded domain in the complex plane. Namely, we show that for any strictly convex bounded $D\subset\mathbb{C}$ of class C² if we fix $\zeta$ in the boundary of $D$ and consider the Cauchy Kernel Function</p> <p>\mathcal{K}(\zeta,z)=\frac{1}{2\pi i}\frac{1}{\zeta-z}</p> <p>as a function of $z$, then the Cauchy Kernel Function belongs to the Smirnov class E^q(D) for every $q\in(0,1)$.</p>

Name thesis:degree_name

Doctor of Philosophy in Mathematics (PhD)

Level thesis:degree_level

Dissertation

Year dc:date.available

2013

Author dc:creator

• Espinosa Lucio, Belen

Advisor dc:contributor.advisor

• Lanzani, Loredana

Contributors dc:contributor

• Harrington, Phillip S.
• Luecking, Daniel H.

• Pure sciences
• Applied sciences
• Cauchy kernel
• Complex variables
• Hardy spaces
• Smirnov space
• Numerical Analysis and Computation

Repository record dc:identifier

https://scholarworks.uark.edu/etd/766

OAI identifier oai:identifier

oai:scholarworks.uark.edu:etd-1765