We obtain sharp ranges of $L^p$-boundedness for domains in a wide class Reinhardt representable as sub-level sets monomials, by expressing them quotients simpler domains. prove general transformation law relating on domain and its quotient finite group. The range $p$ which the Bergman projection is $L^p$-bounded our found to shrink complexity increases.

In this paper, we introduce a dyadic structure on convex domains of finite type via the so-called flow tents. This allows us to establish weighted norm estimates for Bergman projection P such with respect Muckenhoupt weights. particular, result gives an alternative proof $$L^p$$ boundedness P. Moreover, using extrapolation, are also able derive vector-valued and modular inequalities projection.

Let Ω ⊂⊂ C be a domain with smooth boundary, whose Bergman projection B maps the Sobolev space H1(Ω) (continuously) into H2(Ω). We establish two smoothing results: (i) the full Sobolev norm ‖Bf‖k2 is controlled by L derivatives of f taken along a single, distinguished direction (of order ≤ k1), and (ii) the projection of a conjugate holomorphic function in L(Ω) is automatically in H2(Ω). There ...

Received 13 June 2008; Revised 12 October 2008; Accepted 20 November 2008 Recommended by Stevo Stevic This paper shows that if S is a bounded linear operator acting on the weighted Bergman spaces Aα on the unit ball in C n such that STzi TziS i 1, . . . , n , where Tzi zif and Tzi P zif ; and where P is the weighted Bergman projection, then S must be a Hankel operator. Copyright q 2008 Y. Lu an...

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 ...