$L^p$ boundedness of the Bergman projection on some generalized Hartogs triangles

A study of the Bergman projection in certain Hartogs domains

We show that the Bergman projection does not preserve smoothness of functions in some pseudoconvex domains in the space of two complex variables.

BOUNDEDNESS OF THE BERGMAN PROJECTIONS ON Lp SPACES WITH RADIAL WEIGHTS

D |f(z)|dμ(z) )︀1/p < ∞ and by La(D, dμ) (or La(D) for short) the subspace of the space L(D) comprising the functions that are analytic on D. If p = 2, La(D) is a Hilbert subspace of L2(D) and it is called Bergman space. Let P denote the orthogonal projector of L2(D) on La(D) (Bergman projection). Let {δn}n=0 be defined by δn = (︀ 2π ∫︀ 1 0 r 2n+1w(r) dr )︀1/2 . Then, the sequence of functions ...

Weighted Bergman projections on the Hartogs triangle: exponential decay

We study weighted Bergman projections on the Hartogs triangle in C. We show that projections corresponding to exponentially vanishing weights have degenerate L mapping properties.

Zeroes of the Bergman kernel of Hartogs domains

We exhibit a class of bounded, strongly convex Hartogs domains with realanalytic boundary which are not Lu Qi-Keng, i.e. whose Bergman kernel function has a zero.

Boundedness of the Bergman Type Operators on Mixed Norm Spaces

Conditions sufficient for boundedness of the Bergman type operators on certain mixed norm spaces Lp,q(φ) (0 < p < 1, 1 < q <∞) of functions on the unit ball of Cn are given, and this is used to solve Gleason’s problem for the mixed norm spaces Hp,q(φ) (0 < p < 1, 1 < q <∞).

The Bergman Projection on Sectorial Domains