We establish characterizations of the radial weights ? on unit disc such that Bergman projection P?, induced by ?, is bounded and/or acts surjectively from L? to Bloch space B, or dual weighted A?1 isomorphic under A?2-pairing. also solve problem posed Dostani? in 2004 describing P? Lebesgue L?p, a weak regularity hypothesis weight involved. With regard Littlewood-Paley estimates, we characteri...

We show that the norm of the Bergman projection on L of the unit ball in C is comparable to csc(π/p) for 1 < p <∞.

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

Let ϕ be a real-valued plurisubharmonic function on [Formula: see text] whose complex Hessian has uniformly comparable eigenvalues, and let [Formula: see text] be the Fock space induced by ϕ. In this paper, we conclude that the Bergman projection is bounded from the pth Lebesgue space [Formula: see text] to [Formula: see text] for [Formula: see text]. As a remark, we claim that Bergman projecti...

We give various equivalent formulations to the (partially) open problem about Lboundedness of Bergman projections in tubes over cones. Namely, we show that such boundedness is equivalent to the duality identity between Bergman spaces, A ′ = (Ap)∗, and also to a Hardy type inequality related to the wave operator. We introduce analytic Besov spaces in tubes over cones, for which such Hardy inequa...

A function f ∈ C(Ω) is holomorphic on Ω, if it satisfies the CauchyRiemann equations: ∂̄f = ∑n k=1 ∂f ∂z̄k dz̄k = 0 in Ω. Denote the set of holomorphic functions on Ω by H(Ω). The Bergman projection, B0, is the orthogonal projection of square-integrable functions onto H(Ω)∩L2(Ω). Since the Cauchy-Riemann operator, ∂̄ above, extends naturally to act on higher order forms, we can as well define Bergm...

We study the Bergman kernel and projection on the worm domains Dβ = { ζ ∈ C : Re ( ζ1e −i log |ζ2| 2) > 0, ∣∣ log |ζ2| ∣∣ < β − π 2 } and D β = { z ∈ C : ∣Im z1 − log |z2| ∣∣ < π 2 , | log |z2| | < β − π 2 } for β > π. These two domains are biholomorphically equivalent via the mapping D β ∋ (z1, z2) 7→ (e z1 , z2) ∋ Dβ . We calculate the kernels explicitly, up to an error term that can be contr...