Regularity of the Szegö projection on model worm domains

In this paper, we study the regularity of the Szego projection on Lebesgue and Sobolev spaces on the boundary of the unbounded model worm domain D'(beta). We consider the Hardy space H-2( D'(beta)). Denoting by bD'(beta) the boundary of D'(beta), it is classical that H-2(D'(beta)) can be identified with the closed subspace of L-2(bD'(beta), d sigma), denoted by H-2(bD'(beta)), consisting of the boundary values of functions in H-2(D'(beta)), where ds is the induced Lebesgue measure. The orthogonal Hilbert space projection P : L-2(bD'(beta), d sigma) -> H-2(bD'(beta)) is called the Szego projection. Let Ws, p(bD'(beta)) denote the Lebesgue-Sobolev space on bbD'(beta). We prove that P, initially defined on the dense subspace W-s,W-p(bD'(beta)) boolean AND L-2(bD'(beta), d sigma), extends to a bounded operator P : W-s,W-p(bD'(beta)) -> W-s,W-p(bD'(beta)), for 1 < p < infinity and s >= 0.