2016/02/08 by Monguzzi, Alessandro, Peloso, Marco M.
#Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.1602.02615
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 D'β. We consider the Hardy space H2(D'β). Denoting by bD'β the boundary of D'β, it is classical that H2(D'β) can be identified with the closed subspace of L2(bD'β,dσ), denoted by H2(bD'β), consisting of the boundary values of functions in H2(D'β), where dσ is the induced Lebesgue measure. The orthogonal Hilbert space projection P: L2(D'β,dσ)→ H2(bD'β) is called the Szegö projection. Let Ws,p(bD'β) denote the Lebesgue--Sobolev space on bD'β. We prove that P, initially defined on the dense subspace Ws,p(bD'β)∩ L2(bD'β,dσ), extends to a bounded operator P: Ws,p(bD'β)→ Ws,p(bD'β), for 1