Regularity of the Szegö projection on model worm domains

In this paper, we study the regularity of the Szegö projection on Lebesgue and Sobolev spaces on the boundary of the unbounded model worm domain bD'β.We consider the Hardy spaceH2(D'β). Denoting by bD'β.the boundary ofD'β, it is classical thatcan be identified with the closed subspace of L2(D'β, dσ), denoted by H2(D'β), consisting of the boundary values of functions in H2(D'β), where P : L2(D'β, dσ) →H2(D'β) is the induced Lebesgue measure. The orthogonal Hilbert space projection Ws,p (bD'β.) is called the Szegö projection. Letdenote the Lebesgue–Sobolev space on bD'β. We prove that P, initially defined on the dense subspace Wsp(bD'β)∩ L2(D'β, dσ), extends to a bounded operatorP : Wsp(bD'β)→ Wsp(bD'β) and 1 < p < ȡEand s ≥ 0