Regularity of projection operators attached to worm domains

TL;DR

This paper constructs a projection operator for an unbounded worm domain that preserves certain Sobolev subspaces defined by Fourier decomposition, advancing understanding of function space regularity on complex domains.

Contribution

It introduces a new projection operator tailored to the unbounded worm domain, preserving Sobolev subspaces based on rotational symmetry, which was not previously established.

Findings

The projection operator maps subspaces of W^s to themselves.

The operator respects the Fourier decomposition related to rotational invariance.

This work enhances the understanding of regularity properties on worm domains.

Abstract

We construct a projection operator on an unbounded worm domain which maps subspaces of $W^s$ to themselves. The subspaces are determined by a Fourier decomposition of $W^s$ according to a rotational invariance of the worm domain.