# On Existence of Boundary Values of Polyharmonic Functions

## TL;DR

This paper characterizes the boundary behavior of polyharmonic functions inside the unit disk, establishing conditions for their boundary values to exist in hyperfunction spaces.

## Contribution

It provides a comprehensive description of boundary values of polyharmonic functions in terms of hyperfunctions and specifies conditions for these boundary values to belong to particular subspaces.

## Key findings

- Boundary values exist in the space of hyperfunctions.
- Necessary and sufficient conditions for boundary value belonging to subspaces.
- Complete description of polyharmonic functions inside the unit disk.

## Abstract

In trigonometric series terms all polyharmonic functions inside the unit disk are described. For such functions it is proved the existence of their boundary values on the unit circle in the space of hyperfunctions. The necessary and sufficient conditions are presented for the boundary value to belong to certain subspaces of the space of hyperfunctions.