## Date of Graduation

5-2024

## Document Type

Dissertation

## Degree Name

Doctor of Philosophy in Mathematics (PhD)

## Degree Level

Graduate

## Department

Mathematical Sciences

## Advisor/Mentor

Raich, Andrew

## Committee Member

Harrington, Phillip S.

## Second Committee Member

Bradshaw, Zachary

## Keywords

Atomic Decomposition; Boundary Values in the Sense of Distributions; Hardy Spaces; Meta-Analytic Functions; Nonhomogeneous Cauchy-Riemann Equations; Schwarz Boundary Value Problem

## Abstract

We prove that many of the boundary properties associated with functions in the classic holomorphic Hardy spaces on the complex unit disk are present in Hardy classes of solutions to certain nonhomogeneous Cauchy-Riemann equations and higher-order generalizations of these equations. Also, we explicitly solve generalizations of the Schwarz boundary value problem on the complex unit disk and the upper-half plane when the boundary condition is in terms of boundary values in the sense of distributions.

## Citation

Blair, W. L.
(2024). Generalizations of the Hardy Spaces and the Schwarz Boundary Value Problem. * Graduate Theses and Dissertations*
Retrieved from https://scholarworks.uark.edu/etd/5217

#### Included in

Atomic, Molecular and Optical Physics Commons, Control Theory Commons, Special Functions Commons