Lp -estimates for the Bergman projection on strictly pseudoconvex nonsmooth domains

On proper harmonic maps between strictly pseudoconvex domains with Kähler metrics of Bergman type

where (h) is the inverse of the matrix (hij), ∆M = ∑ i,j h ∂ij and Γ s tγ denote the Christoffel symbols of the Hermitian metric g on N . It follows from (1.1) that if u is holomorphic, then u must be harmonic. Thus, it is natural to ask under what circumstances a harmonic map is holomorphic or antiholomorphic. Under the assumption that both M and N are compact, Siu [31] demonstrated that if th...

Scattering Theory for Strictly Pseudoconvex Domains

The spectral theory of a metric of Bergman type on a strictly pseudoconvex manifold is described and the scattering matrix is shown to be a pseudodifferential operator of Heisenberg type.

Pseudolocal Estimates for ∂̄ on General Pseudoconvex Domains

Extending the well-known results for smoothly bounded case, we show that subelliptic and pseudolocal estimates hold in the neighbourhood of a smooth strictly pseudoconvex (or finite type) boundary point of any pseudoconvex domain (i.e. possibly unbounded or with nonsmooth boundary). As an application, we also prove the corresponding generalization of Kerzman’s and Fefferman-Boutet de Monvel-Sjö...

The Bergman Projection on Sectorial Domains

Sobolev Space Projections in Strictly Pseudoconvex Domains

The orthogonal projection from a Sobolev space WS(Q) onto the subspace of holomorphic functions is studied. This analogue of the Bergman projection is shown to satisfy regularity estimates in higher Sobolev norms when ß is a smooth bounded strictly pseudoconvex domain in C". The Bergman projection P0: L2(ü) -» L2(S2) n {holomorphic functions}, where S2 c C" is a smooth bounded domain, has prove...